ORAL  EXERCISES 

in  NUMBER 
By  Anna  L,  Rice 


z 


M-    . 


GIFT   OF 
R-D  -L1NQUIST 


1 


EDUCATION  DEPT. 


ORAL 
EXERCISES   IN   NUMBER 

FOR  USE  IN  GRADES  FOUR  TO  EIGHT  INCLUSIVE 

BY 

ANNA   L.   RICE 

PRINCIPAL    OF    LINCOLN    SCHOOL,    SPRINGFIELD 

MASSACHUSETTS 

AUTHOR    OF    "OUTLINES    IN    DICTIONARY 

STUDY  " 


THE  GREGG  PUBLISHING  COMPANY 

NEW  YORK  CHICAGO  BOSTON  SAN  FRANCISCO 

LONDON 


COPYRIGHT,     192  1,     BY     THE 
GREGG    PUBLISHING    COMPANY 


Gift 

R.D  .LINQUIST 

EDUCATION  DEPT. 


PREFACE 

Though  educators  differ  as  to  just  how  much  knowledge 
of  arithmetic  is  essential  to  a  common-school  education,  the 
necessity  of  teaching  certain  fundamental  facts  of  number  is 
unquestioned.  Children  must  be  taught  to  add,  subtract,  multiply, 
and  divide,  whole  numbers.  They  must  understand  common 
fractions,  and  be  able  to  perform  the  same  operations  with  these 
as  with  whole  numbers.  Some  knowledge  of  decimals  is  necessary, 
in  order  that  they  may  be  able  to  use  United  States  money.  They 
must  be  acquainted  with  the  common  facts  of  denominate  num- 
bers, and  know  the  elements  of  percentage. 

This  elementary  knowledge  of  number  is  essential  not  only  to 
a  common-school  education,  but  as  a  foundation  for  all  advanced 
work  in  mathematics.  If  this  foundation  is  weak,  the  work  built 
upon  it  will  be  weak;  for  it  is  clear  that  no  problem  can  be 
correctly  solved  if  the  simple  operations  which  it  involves  are 
incorrectly  performed.  Nor  should  we  be  satisfied  with  accuracy 
alone.  The  facts  of  number  are  not  in  any  true  sense  learned  until 
they  can  be  quickly,  as  well  as  accurately,  recalled. 

If  the  teaching  of  the  fundamental  facts  of  number  is  to  be 
effective  —  if  these  simple  number  combinations,  which  are  the 
very  alphabet  of  all  mathematical  work,  are  to  be  mastered  — 
systematic  training  must  be  given.  No  royal  road  to  the 
accomplishment  of  this  end  has  yet  been  found.  Mastery  of  these 
tools  of  the  mind,  like  the  mastery  of  a  musical  instrument,  comes 
through  long-continued  practice  only.  In  other  words,  drill  is 
indispensable. 

Drill  in  arithmetic,  to  be  effective,  must  be  regular.  A  few 
minutes  daily  should  be  devoted  to  it  in  each  grade.     It  must  be 


'^cro  ^  a 


iv  PREFACE 

thorough ;  that  is,  the  facts  need  to  be  presented  over  and  over 
again.  The  method  of  presenting  these  facts  must  also  be  varied 
from  day  to  day,  in  order  to  maintain  interest. 

To  provide  for  this  daily  drill,  an  abundance  of  material  is 
necessary.  The  textbook  in  arithmetic,  however  excellent  it  may 
be,  cannot  fully  supply  this  need. 

Oral  Exercises  in  Number  is  intended  to  supplement  any 
basal  textbook  in  arithmetic,  and  is  adapted  for  use  from  the 
fourth  grade  to  the  high  school.  It  is  not  assumed  that  the  book 
will  be  used  for  more  than  ten  minutes  daily  in  any  grade.  This 
daily  period  of  drill,  if  begun  in  the  fourth  grade,  should  enable 
pupils  to  master  the  essential  facts  of  number  by  the  time  they 
reach  the  seventh  or  the  eighth  grade.  It  is  not  necessary  to 
lengthen  the  arithmetic  period  to  allow  for  this  work,  for  pupils 
will  soon  be  able  to  do  their  written  arithmetic  more  rapidly  as 
the  result  of  this  daily  oral  drill.  As  they  gain  in  accuracy  and 
speed,  and  the  time  now  so  unprofitably  spent  in  looking  for  and 
correcting  mistakes  is  gradually  eliminated,  less  time  will  be  re- 
quired to  teach  the  topics  of  the  higher  grades,  and  children  will 
take  greater  interest  and  pleasure  in  their  work.  For  every  one 
enjoys  doing  the  things  he  can  do  well,  while  failure  is  discouraging 
to  us  all. 

As  indicated  by  the  spacing  the  exercises  on  most  of  the  pages 
are  graded,  the  first  group  of  exercises  on  each  page  being  the 
simplest.  It  is  not  possible,  however,  to  say  definitely  what 
exercises  should  be  used  in  a  given  grade.  This  must  be  de- 
termined by  the  ability  of  the  children,  and  by  what  has  already 
been  mastered.  In  using  these  graded  pages,  teachers  should  be 
guided  by  the  following  rule : 

"  Master  the  first  group  of  exercises  on  any  page  before  taking 
the  second,  and  master  the  second  group  before  taking  the  third.' ' 

The  ungraded  pages  are  of  about  equal  difficulty  throughout, 
and  require  no  explanation. 


PREFACE  V 

It  is  expected  that  teachers  will  use  the  exercises  suited  to  their 
grades  not  simply  once  or  twice,  but  many  times.  The  same 
exercise  should  not,  however,  be  used  on  two  or  more  consecutive 
days.  This  would  mean  loss  of  interest,  and  possible  memorizing 
of  answers.  Since  one  exercise  affords  as  good  mental  drill  as 
another,  the  power  gained  by  spending  ten  minutes  on  any  exercise 
will  help  pupils  to  master  any  other.  After  going  through  an 
exercise  once  or  twice  leave  it  for  a  different  one,  coming  back 
to  it  from  time  to  time  until  children  have  no  further  need  of  it. 

A  study  of  the  mistakes  made  by  children  in  their  arithmetical 
work  shows  that  some  number  facts  are  remembered  with  greater 
difficulty  than  others.  The  most  troublesome  combinations  occur 
most  frequently  on  the  pages  of  this  book. 

Since  variety  is  as  important  a  factor  in  effective  drill  as  repe- 
tition, the  same  old  number  facts  are  dressed  in  new  costumes 
and  introduced  under  different  headings,  such  as  "  United  States 
Money/'  "  Denominate  Numbers,"  "  Percentage,"  etc.  An  im- 
portant by-product  of  this  method  of  drill  will  be  the  familiarity 
thus  acquired  by  pupils  with  the  elements  of  these  subjects. 

While  the  object  of  these  exercises  is  to  develop  both  accuracy 
and  speed,  teachers  should  never  lose  sight  of  the  fact  that  chil- 
dren are  to  be  trained  to  accuracy  first.  Do  not  confuse  them 
by  trying  to  secure  speed  and  accuracy  at  the  same  time.  An 
exercise  should  be  well  learned  before  children  are  timed  in  recit- 
ing it. 

Much  interest  can  be  aroused  in  number-drills,  and  the  value  of 
these  drills  will  be  in  proportion  to  the  interest  and  enthusiasm  of 
the  class.  An  appeal  to  the  play  instinct  meets  with  instant  re- 
sponse from  children,  who  love  to  compete  with  each  other  in  doing 
mental,  as  well  as  physical,  stunts.  Teachers  will  find  these  ex- 
ercises well  adapted  for  group  work,  and  class  drills  should  be  sup- 
plemented by  much  work  of  this  kind.  A  few  suggestions  for 
making  the  drills  interesting  will  be  found  on  another  page. 


VI  PREFACE 

The  author  gratefully  acknowledges  her  indebtedness  to  Dr. 
James  H.  Van  Sickle,  Superintendent  of  Schools,  Springfield, 
Massachusetts;  to  Dr.  G.  M.  Wilson,  Professor  of  Education, 
Iowa  State  College;  and  to  Miss  Sarah  J.  Lee,  formerly  teacher 
of  mathematics  in  the  High  School,  Riverside,  California,  for 
their  courtesy  in  reviewing  this  text  and  for  their  many  helpful 
criticisms  and  suggestions. 

A.  L.  R. 


HOW   NUMBER-DRILLS   MAY  BE  MADE 
INTERESTING 

Hints  to  Teachers 

The  purpose  of  this  book,  as  stated  in  the  preface,  is  to  supply 
teachers  in  elementary  and  junior  high  schools  with  material  for 
oral  drill  in  the  fundamental  facts  of  number.  Since  the  value 
of  this  drill  will  depend  largely  upon  the  way  in  which  the  book 
is  used,  it  is  hoped  that  teachers  will  first  of  all  read  the  preface, 
in  order  to  acquaint  themselves  with  the  principles  upon  which 
the  book  is  based,  the  arrangement  of  material,  and  the  manner 
in  which  the  exercises  are  intended  to  be  used. 

It  is  suggested  that  teachers  supplement  class  drill  by  much 
group  work.  This  method  of  study  is  particularly  interesting 
and  effective  when  used  as  a  means  of  preparation  for  the  one- 
minute  exercises  and  speed  tests  suggested  further  on.  As  a  rule, 
only  exercises  which  have  been  studied  in  class  should  be  assigned 
for  group  work,  and  the  leader  of  each  group  should  be  a  pupil 
who  has  accurately  recited  the  exercise  chosen  for  study.  Any 
member  of  the  group  may,  however,  question  the  correctness 
of  an  answer  accepted  by  the  leader,  and  the  group  as  a  whole 
must  be  convinced  that  the  answer  finally  accepted  is  right. 

The  value  of  group  work  depends  upon  the  keen  participation 
of  each  member  of  the  group  in  the  work  being  done,  and  each 
pupil  should  feel  a  sense  of  personal  responsibility  for  noticing 
errors.  Considerable  freedom  is  t  therefore  necessary,  but  no 
disorder.  It  is  quite  possible  for  several  groups  to  work  at  the 
same  time  without  disturbing  one  another  or  the  teacher  in  the 
least.  It  will  add  to  the  independence  of  pupils  if  they  learn 
where  to  find,  in  their  textbook  in  arithmetic,  the  multiplication 


Vlll  HINTS  eTO   TEACHERS 

tables  and  the  tables  of  denominate  numbers,  and  form  the  habit 
of  referring  to  these  tables  whenever  in  doubt  about  the  facts 
which  are  to  be  found  stated  in  them. 

On  pages  84  and  124  will  be  found  a  few  suggestions  for  one- 
minute  exercises  and  speed  tests,  indicating  ways  in  which  almost 
any  exercise  may  be  used  after  it  has  been  sufficiently  practiced. 

Pupils  should  frequently  be  allowed  to  choose  the  exercise  for 
study.  A  few  minutes'  drill  on  this  exercise  will  show  each 
member  of  the  class  where  his  own  weakness  lies,  and  after  a 
period  of  study  —  preferably  in  groups  —  individuals  may  be 
timed  in  reciting  either  the  whole  exercise  or  some  part  of  it. 
Or,  a  row  of  pupils,  each  in  turn  answering  one  question,  may 
compete  with  another  row  reciting  in  the  same  manner. 

Another  suggestion  is  that  a  boy*  be  chosen  by  the  boys  and 
a  girl  by  the  girls  to  compete  with  each  other,  answering  ques- 
tions alternately  from  a  given  exercise.  If  the  boy  makes  a 
mistake  the  girls  win,  and  vice  versa.  If  neither  one  makes  a 
mistake,  it  is  a  tie.  Another  boy  and  girl  are  then  chosen,  and 
the  game  proceeds  as  before. 

Still  another  suggestion  is  that  a  game  like  the  old-fashioned 
spelling  match  be  made  of  these  exercises,  the  pupils  being  evenly 
divided  on  "sides."  The  teacher  should  choose  simple  exercises 
for  this  game,  and  should  put  the  questions  herself. 

As  teachers  become  familiar  with  the  contents  of  this  book, 
they  will  develop  methods  of  drill  better  suited,  perhaps,  to  the 
needs  of  their  classes  than  any  here  suggested.  The  important 
fact  to  keep  in  mind  is  that  the  only  good  drill  is  a  lively  one. 
The  success  of  any  drill  is  measured  by  the  degree  of  interest 
aroused. 


CONTENTS 

PAGE 

Whole  Numbers 1  to  60 

Addition 1 

Subtraction 18 

Addition  and  Subtraction     .         .         .         .         0         .         .         .  23 

Multiplication 26 

Facts  of  the  Multiplication  Tables 37 

Multiplication  and  Addition 38 

Multiplication  and  Subtraction     .......  39 

Division 40 

Facts  of  the  Division  Tables 48 

Multiplication  and  Division  .         .         .         .         .         .         .49 

Practice  in  Interpreting  Signs  Quickly 50 

Relation  of  Numbers 53 

Cancellation 54 

Factoring 58 

Numbers  —  Prime  and  Composite 59 

Factors  and  Multiples  . 60 

Common  Fractions 61  to  83 

Reduction ' 61 

Comparison 66  and  76 

Addition 67 

Subtraction 70 

Addition  and  Subtraction 73 

Multiplication 74 

Fractional  Parts  of  Numbers 79 

Division 81 

Special  One-minute  Exercises   .        .        .        .  .        .        .84 

United  States  Money 85  to  96 

U.  S.  Coins 85 

Addition 86 

Finding  Amount  of  Purchases 87 

ix 


X  CONTENTS 

PAGE 

Subtraction  —  Making  Change     .         .         .         .         .         .         .88 

Fractional  Parts  of  One  Dollar 91 

The  Number  Twenty-Five 96 

Decimal  Fractions 97  to  108 

Addition 97 

Subtraction 100 

Multiplication ..103 

Division 106 

Denominate  Numbers 109  to  113 

Reckoning  Time 113 

Percentage .  114  to  119 

Percentage  and  Denominate  Numbers 120  to  123 

Speed  Tests  in  Percentage 124 

Areas  and  Perimeters 125 

Appendix 126  to  135 

Reading  of  Whole  Numbers 127 

Reading  Exercise :  U.  S.  Money 129 

Reading  Exercise :  Roman  Numerals    .         ...         .         .  130 

Months  and  Dates 131 

Relation  of  Numbers,  or  Ratio 132 

Questions  for  Leisure  Moments 133 


WHOLE  NUMBERS    ADDITION 
1.    1  and  2  2.  4  +  3  3.   3  and  4  4.  6  +  5 


5  and  2 

7  +  3 

5  and  4 

2  +  5 

4  and  2 

3  +  3 

1  and  4 

1  +  5 

7  and  2 

8  +  3 

0  and  4 

7  +  5 

3  and  2 

9  +  3 

6  and  4 

8  +  5 

9  and  2 

0  +  3 

8  and  4 

3  +  5 

8  and  2 

2  +  3 

2  and  4 

9  +  5 

2  and  2 

6  +  3 

9  and  4 

0  +  5 

6  and  2 

1  +  3 

4  and  4 

4  +  5 

0  and  2 

5  +  3 

7  and  4 

5  +  5 

5.  10  +  4 

6.  20  +  2 

7.  30  +  5 

8.  40  +  3 

11  +  3 

21  +  5 

31  +  2 

41  +  4 

12  +  3 

22  +  2 

32  +  4 

42  +  5 

13  +  4 

23  +  3 

33  +  2 

43  +  5 

14  +  2 

24  +  5 

34  +  3 

44  +  4 

15  +  5 

25  +  2 

35  +  4 

45  +  3 

16  +  2 

26  +  3 

36  +  5 

46  +  4 

17  +  5 

27  +  4 

37  +  3 

47  +  2 

18  +  3 

28  +  5 

38  +  2 

48  +  4 

19  +  4 

29  +  3 

39  +  5 

8 

49  +  2 

Id: 
9.  5    6 

4 

3    6 

10.  7    3 

6    2 

4    6 

8 

9    0 

5    6 

8 

7    5 

9    2 

7 

7    8 

2    9 

4 

8   9 

11.  3    9 

6 

3    5 

12.  3    2 

7 

6    9 

7    5 

4 

7    0 

9    2 

3 

7    0 

6    8 

9 

7    8 

9    7 

3 

8    7 

13.  1    3 

2 

1    2 

14.  6    5 

8 

4    7 

2    0 

4 

5    8 

6    7 

5 

4    7 

8    9 

5 

9    6 

1 

6    5 

8 

4    7 

2                            WHOLE   NUMBERS 

ADDITION 

1.    6  plus  6 

2.     3  +  7 

3. 

5  and  8 

4.      1  +  9 

0  plus  6 

6  +  7 

9  and  8 

4  +  9 

3  plus  6 

9  +  7 

1  and  8 

0  +  9 

1  plus  6 

2  +  7 

7  and  8 

9  +  9 

5  plus  6 

4  +  7 

2  and  8 

6  +  9 

2  plus  6 

8  +  7 

8  and  8 

2  +  9 

9  plus  6 

1  +  7 

3  and  8 

8  +  9 

8  plus  6 

5  +  7 

0  and  8 

3  +  9 

7  plus  6 

7  +  7 

4  and  8 

7  +  9 

4  plus  6 

0  +  7 

6  and  8 

5  +  9 

5.   50  +  8 

6.    60  +  9 

7. 

70  +  6 

8.   80  +  7 

51  +  6 

61  +  7 

71  +  8 

81  +  9 

52  +  7 

62  +  8 

72  +  9 

82  +  6 

53  +  7 

63  +  8 

73  +  9 

83  +  6 

54  +  9 

64  +  7 

74  +  6 

84  +  8 

55  +  7 

65  +  9 

75  +  6 

85  +  8 

56  +  6 

66  +  8 

76  +  9 

86  +  7 

57  +  8 

67  +  7 

77  +  6 

87  +  9 

58  +  9 

68  +  8 

78  +  7 

88  +  6 

59  +  6 

69  +  9 

79  +  8 

89  +  7 

Add: 

9.   5        3 

9 

2        5 

10 

6        3 

8 

7        9 

4        8 

0 

4        1 

7        2 

7 

1         2 

6        7* 

7 

6        0 

6        5 

8 

0        9 

2        2 

1 

8        9 

7        8 

7 

8        2 

11.    2        3 

7 

8        6 

12 

9        3 

2 

3        9 

8        5 

7 

8        6 

2        5 

2 

8        6 

0        6 

9 

4        3 

0        4 

9 

8        4 

9        8 

9 

4        3 

7        8 

5 

2         1 

WHOLE  NUMBERS 

ADDITION 

3 

1. 

1 

2 

3 

4 

5 

2. 

6 

7 

8 

9 

0 

6 

5 

4 

5 

8 

5 

9 

9 

2 

7 

3. 

1 

2 

3 

4 

5 

4. 

6 

7 

8 

9 

6 

4 

9 

6 

9 

7 

7 

6 

4 

4 

6 

5. 

1 

2 

3 

4 

5 

6. 

6 

7 

8 

9 

0 

7 

6 

5 

2 

9 

8 

7 

8 

3 

9 

7. 

1 

2 

3 

4 

5 

8. 

6 

7 

8 

9 

7 

8 

7 

8 

4 

1 

9 

4 

7 

9 

2 

9. 

8 

9 

3 

4 

5 

10. 

7 

2 

5 

1 

6 

2 

1 

7 

6 

5 

3 

8 

5 

9 

4 

11. 

3 

7 

4 

5 

5 

12. 

4 

2 

1 

9 

3 

3 

2 

4 

3 

4 

0 

2 

8 

0 

6 

4 

1 

2 

2 

1 

6 

6 

1 

1 

1 

13. 

7 

3 

4 

8 

6 

14. 

3 

9 

8 

9 

4 

5 

1 

2 

•  7 

6 

5 

4 

5 

6 

9 

2 

9 

6 

3 

3 

3 

4 

7 

3 

7 

15. 

7 

9 

3 

4 

8 

16. 

5 

8 

7 

6 

4 

8 

2 

4 

7 

8 

4 

2 

3 

8 

5 

6 

5 

6 

5 

2 

5 

3 

5 

6 

8 

17. 

2 

5 

6 

5 

3 

18. 

6 

2 

4 

6 

1 

8 

9 

0 

1 

3 

8 

9 

8 

3 

8 

3 

7 

4 

7 

2 

4 

1 

5 

2 

4 

1 

2 

8 

7 

8 

9 

7 

5 

4 

7 

19. 

5 

7 

8 

4 

2 

20. 

6 

5 

3 

7 

3 

8 

9 

6 

6 

2 

4 

0 

8 

7 

9 

7 

5 

1 

3 

8 

3 

5 

3 

2 

6 

6 

3 

9 

7 

9 

3 

9 

n 

4 

5 

WHOLE  NUMBERS       ADDITION 

1.    1  +  6  2.    1  +  4  3.    1  +  7                   4.    1  +  9 

2  +  5  2  +  8  2  +  6  2  +  7 

3  +  4  3  +  6  3  +  5  3  +  8 

4  +  6  4  +  9  4  +  8  4  +  4 

5  +  8  5  +  2  5  +  3  5  +  5 

6  +  4  6  +  7  6  +  8  6  +  9 

7  +  9  7  +  3  7  +  2  7  +  4 

8  +  6  8+4  8  +  5  8  +  7 

9  +  2  9  +  5  9  +  4  9  +  9 
0  +  7  0  +  0  0  +  9  0  +  2 


Add: 

5. 

13 

24 

49 

27 

6.  12 

39 

73 

44 

5 

6 

8 

6 

2 

5 

8 

7 

7. 

65 

34 

19 

51 

8.  77 

66 

55 

13 

_8 

5 

6 

5 

7 

6 

8 

7 

9. 

33 

42 

87 

91 

10.  75 

69 

25 

48 

_8 

8 

5 

7 

4 

8 

6 

4 

11.  5    3    8    6    4  12.  6    2    6    5    3 

67031  78083 

02873  17382 

49428  35802 

51^52  12    14    4 

13.  3    4    7    8    6  14.  7    3    2    1    9 

90836  84    4    30 

86152  05658 

26902  36072 

2    3    295  77814 


WHOLE  NUMBERS       ADDITION  5 

1.    1  +  5  2.    5+1  3.    8  +  8                   4.    2  +  3 

9  +  7  2  +  4  1  +  8  7  +  5 

4  +  5  6  +  5  9  +  6  9  +  1 
3  +  7..  7  +  7  7  +  6  3  +  9 
2  +  9  8+1  5  +  9  8  +  9 

5  +  6  9  +  8  2  +  3  6  +  3 
8  +  3  4  +  7  4  +  3  4  +  2 
7  +  8  3  +  2  6  +  2  7  +  5 
4+1  5  +  7  3  +  3  5  +  4 

6  +  6  7+1  8  +  2  9  +  3 


Add: 

5. 

24 

16 

44 

57 

6. 

42 

50 

29 

19 

12 

32 

22 

30 

26 

18 

10 

50 

7. 

75 

38 

73 

61 

8. 

15 

46 

64 

70 

11 

40 

24 

17 

31 

12 

33 

25 

9. 

25 

16 

80 

21 

10. 

15 

35 

49 

36 

42 

31 

19 

23 

51 

42 

30 

41 

11.   7        8        3        6        2  12.   9 


1 

0 

3 

4 

2 

4 

8 

9 

3 

4 

3 

2 

8 

9 

8 

5 

4 

7 

0 

4 

6 

5 

2 

7- 

2 

4 

6 

5 

3 

5 

3 

1 

6 

3 

4 

3 

7 

4 

3 

1 

4 

2 

5 

1 

2 

2 

8 

2. 

1 

7 

2 

9 

3 

2 

1 

13.   4         6         5         3         5  14.    8 


0 

7 

1 

2 

6 

1 

4 

8 

3 

5 

6 

2 

7 

8 

2 

7 

0 

6 

0 

5 

9 

8 

3 

8 

1 

8 

2 

3 

9 

6 

3 

5 

2 

8 

5 

7 

6 

5 

7 

4 

6 

9 

4 

6 

3 

5 

8 

7 

5 

2 

7 

4 

6 

4 

1 

6 

WHOLE  NUMBERS 

ADDITION 

Add: 

1. 

9    7 

3 

8 

6 

2.  5    8 

4 

2    9 

8    6 

4 

2 

9 

5    6 

5 

7    5 

3. 

7    5 

6 

8 

9 

4.  9    8 

5 

6    4 

9    4 

6 

0 

3 

9    3 

7 

9    7 

5. 

8    7 

4 

2 

5 

6.  1    8 

5 

6    7 

8   7 

6 

9 

8 

9    7 

0 

5    3 

13  +  4 

10 

7. 

8. 

62 

plus  2 

9.  17  +  7 

.  36  +  6 

27  +  9 

45 

plus  4 

19  +  6 

22  +  7 

84  +  6 

37 

plus  3 

38  +  5 

33  +  8 

55  +  8 

89 

plus  7 

23  +  4 

44  +  9 

31  +  5 

52 

plus  5 

14  +  9 

55  +  8 

42  +  8 

21 

plus  9 

66  +  8 

66  +  7 

26  +  5 

93 

plus  8 

43  +  7 

77  +  6 

57  +  7 

64 

plus  6 

29  +  3 

88  +  5 

45  +  3 

33 

plus  5 

34  +  5 

19  +  4 

78  +  6 

88  plus  8 

50  +  6 

26  +  3 

Add: 
11. 

50   30 

60 

4C 

)      20 

12.  70   80 

10 

90   50 

10   20 

80 

4( 

)   50 

10   20 

40 

20   50 

13. 

55 

37 

64 

43 

22 

14. 

74 

83 

14 

95 

58 

10 

20 

30 

40 

50 

10 

20 

40 

20 

50 

15. 

55 

37 

64 

43 

22 

16. 

74 

83 

14 

95 

58 

13 

21 

32 

44 

56 

12 

25 

44 

22 

51 

17. 

64 

81 

45 

73 

26 

18. 

18 

54 

83 

44 

75 

35 

16 

24 

15 

32 

31 

32 

16 

30 

11 

WHOLE  NUMBERS 

ADDITION 

7 

1.  15  +  2 

2. 

64  +  3 

3.  52  +  4 

4.  75  +  5 

21  +  2 

27  +  3 

25  +  4 

48  +  5 

36  +  2 

35  +  3 

44  +  4 

33  +  5 

45  +  2 

91  +  3 

88  +  4 

56  +  5 

18  +  2 

84  +  3 

16  +  4 

67  +  5 

57  +  2 

36  +  3 

22  +  4 

71  +  5 

64  +  2 

72  +  3 

53  +  4 

74  +  5 

33  +  2 

29  +  3 

92  +  4 

39  +  5 

12  +  2 

43  +  3 

37  +  4 

82+5 

49  +  2 

48  +  3 

41  +  4 

54  +  5 

Add: 

5.  67   24 

36 

50   28 

6.  41   54 

65   63   19 

3    2 

4 

5    3 

5    2 

4    2    5 

7.   37      45      92      69       11  8.   84      94      37      81       35 

A    A    A    A    A  A    A    A    A    A 

9.   49      27      38       16      27  10.   39       58      87       76      92 

45354  23453 


11. 


78 

37 

89 

93 

56 

12.  68 

77 

88 

29 

18 

5 

4 

5 

2 

3 

5 

4 

_3 

2 

_5 

13. 

44 

81 

25 

52 

14. 

88 

39 

42 

53 

36 

49 

36 

39 

52 

17 

29 

38 

15. 

53 

49 

68 

48 

16. 

57 

72 

95 

81 

25 

27 

33 

44 

12 

33 

55 

47 

17. 

25 

37 

82 

58 

18. 

24 

36 

54 

28 

58 

70 

35 

37 

47 

63 

45 

69 

19. 

19 

28 

39 

56 

20. 

45 

82 

16 

44 

34 

63 

29 

36 

37 

94 

65 

37 

8  WHOLE  NUMBERS      ADDITION 

1.  15  +  6  2.  64  +  7  3.  52  +  8      4.  75  +  9 

21  +  6  27  +  7  25  +  8  48  +  9 

36  +  6  35  +  7  44  +  8  33  +  9 

45  +  6  91  +  7  88  +  8  56  +  9 

18  +  6  84  +  7  16  +  8  67  +  9 

57  +  6  36  +  7  22  +  8  71  +  9 

64  +  6  72  +  7  53  +  8  74  +  9 

33  +  6  29  +  7  92  +  8  39  +  9 

12  +  6  43  +  7  37  +  8  82  +  9 

49  +  6  48  +  7  41  +  8  54  +  9 


Add: 


5. 

67 

24 

36 

50 

28 

6. 

41 

54 

65 

63 

19 

_8 

6 

9 

7 

_8 

7 

_6 

8 

9 

_6 

7. 

37 

45 

92 

69 

11 

8. 

84 

94 

37 

81 

35 

_7 

_7 

_8 

9 

J6 

_8 

6 

_8 

7 

9 

9. 

49 

15 

62 

92 

35 

10. 

27 

12 

35 

63 

84 

_6 

7 

9 

_6 

_8 

_7 

6 

J_ 

8 

6 

11. 

75 

37 

46 

73 

52 

12. 

39 

84 

28 

45 

81 

_8 

_6 

_9 

_7 

J_ 

_8 

_6 

_8 

_6 

_9 

13. 

36 

44 

85 

23 

92 

14. 

51 

27 

44 

66 

18 

25 

15 

25 

38 

78 

39 

12 

27 

35 

24 

15. 

81 

37 

25 

48 

92 

16. 

53 

66 

74 

35 

27 

18 

24 

36 

22 

17 

37 

33 

81 

56 

19 

17. 

92 

18 

50 

73 

44 

18. 

55 

87 

77 

85 

74 

72 

23 

65 

27 

36 

15 

29 

60 

25 

j)6 

19. 

58 

27 

33 

81 

28 

20. 

15 

22 

64 

19 

70 

12 

12 

66 

34 

29 

56 

80 

40 

36 

25 

WHOLE  NUMBERS       ADDITION 

To  add  9,  add  10  and  subtract  1. 

15 

2.    66 

3.   34  ; 

4.    24 

23 

44 

45 

36 

67 

33 

•      56 

48 

84 

22 

27 

52 

19 
32 

+  9                35 

78 
^  +  9                89 

+  9 

61 
73 

55 

88 

92 

85 

60 

77 

21 

47 

38 

25 

40 

29 

46, 

30 

13 

70 

+  9 


24  plus  2  plus  5 

13  plus  3  plus  9 

42  plus  4  plus  7 

50  plus  7  plus  8 

12  plus  3  plus  6 

37  plus  9  plus  4 

64  plus  5  plus  2 


6.    32  +  5+  4  +  3 

48  +  3+  7  +  7 

82  +  6+  4  +  5 

35  +  4+  2  +  8 

17  +  7+  5  +  9 

56  +  8+10  +  4 

77  +  3  +  3  +  9 


Note.    The  following  method  of  adding  is    for  higher  grades 
only. 

Learn  to  recognize  at  a  glance  groups  of  figures  which  make  10. 


7.    6 

2 

3 

5 

7 

8.   3 

2 

6 

3 

3 

5 

0 

81 

1 

6 

8 

4 

6 

9 

3 

2 

6 

1 

4 

3 

8' 

3 

3 

6 

4, 

3 

3 

1 

7 

2 

2, 

6 

2 

4. 

2 

7 

1 

7 

6^ 

5. 

1 

9 

4 

2 

9 

4^ 

8 

5 

3 

8 

7 

4 

4, 

8, 

5^ 

3 

9 

2" 

0 

4 

5 

8 

3: 

6 

1 

3, 

3 

6 

1 

7 

9 

1 

7J 

6 

0 

2 

0 

2, 

fr 

0 

6^ 

0 

4 

3 

4 

9 

3 

3 

5, 

9 

2 

1 

4 

1 

7 

1 

4 

6 

8 

5 

2 

4 

1 

4 

7 

10 


WHOLE  NUMBERS      ADDITION 


To  add  11,  add  10  arid  1  more. 


15 
23 
67 
84 
19 
32 
55 
60 
38 
46 


2. 


+  11 


•66  1 

44 

33 

22 

11 

35 

88 

77 

25 

30 


3, 


+  11 


34 
45 
56 

27 
78 
89 
92 
21 
40 
13 


+  11 


24 
36 
48 
52 
61 
73 
85 
47 
29 
70 


+  11 


Add: 


7. 

11,  6, 

5,  and  9. 

6.  13,  9,  and  11. 

8, 

3,  4, 

8,  and  11. 

27,  9,  and  11. 

5, 

8,  3, 

9,  and  2. 

54,  9,  and  11. 

6, 

4,  4, 

11,  and  7. 

62,  9,  and  11. 

•3, 

8,  9, 

5,  and  8. 

39,  9,  and  11. 

4, 

5,  5, 

3,  and  11. 

45,  9,  and  11. 

2, 

6,  8, 

10,  and  3. 

76,  9,  and  11. 

5, 

3,  7, 

9,  and  6. 

28,  9,  and  11. 

Groups  of  figures  which  equal  10  may  be  called  10  in  adding. 


5 

4 

5 

2 

7 

6 

8 

3 

4 

3 

0 

6 

2 

8 

7 

2 

9 

1 

3 

5 

7 

1 

9 

1 

0 

1 

2 

7 

8 

4 

9 

3 

6 

1 

5 

3 

5 

3 

7 

1 

5 

7 

3 

0 

3 

4 

3 

4 

3 

2 

1 

4 

9 

5 

8 

2 
6 
2 
2 
4 
5 
5 
1 
9 
7 
4 


7 
3 
5 
4 
1 
2 
8 
6 
7 
7 


2 
5 
3 
2 

8 
7 
4 
3 
3 
5 
5 


6 
6 
5 
5 
2 
8 
7 
4 
3 
5 
6 


8 
1 
6 
4 
5 
7 
8 
2 
5 
6 
3 


WHOLE  NUMBERS      ADDITION 


11 


+  2 


+  6 


+  11 


2.  22 

3.  86 

4.  85 

59 

21 

62 

63 

32 

49 

91 

90 

37 

87 
44 

^Q          48 

+  3       53 

71 

>  +  4       20 

25 

84 

33 

30 

67 

58 

76 

35 

64 

38. 

29. 

46. 

6.  29 

7.  38^ 

8.  69 

35 

76 

28 

67 

25 

47 

84 

44 

26 

53 

48 

\7       50 

>  +  7       87 

^  +  8       24 

32 

91 

30 

21 

63 

83 

70 

59 

42 

86. 

22. 

31. 

0.  91 

11.  55 

12.  71 

63 

24 

37 

59 

83 

50 

22 

42 

49 

38 
76 

+  U      31 

—  : 

60 

69 

46 

25 

28 

64 

44 

47 

58 

87. 

26. 

33. 

^  +  5 


12 


WHOLE  NUMBERS      ADDITION 


Add: 

1.   5 

8 

7 

4 

4 

2. 

3 

5 

2 

9 

6 

3 

2 

3 

8 

3 

2 

4 

6 

1 

2 

4 

1 

3 

6 

3 

7 

1 

4 

7 

3 

3.   4 

2 

3 

8 

7 

4. 

6 

3 

9 

5 

7 

3 

9 

7 

8 

1 

7 

5 

8 

5 

2 

6 

5 

8 

2 

2 

3 

2 

4 

4 

4 

5.    6 

8 

9 

3 

6 

6. 

2 

1 

5 

7 

4 

6 

3 

4 

2 

2 

7 

6 

4 

6 

2 

4 

2 

5 

9 

2 

7 

3 

6 

5 

8 

~~" 

and  5, 

1, 

add  1( 

For  5 

6  and  4,  7  and  3,  8  and  2,  or  9  and 

J. 

7.    3 

9 

4 

3 

8 

8. 

5 

4 

7 

5 

9 

4^ 

5 

8 

91 

3 

5j 

3 

0 

2 

\\ 

6, 

41 

3 

1J 

91 

1 

21 

3, 

4 

5 

8 

6j 

51 

7 

U 

7 

8j 

5 

0 

8" 

2 

3 

5, 

2 

6^ 

3 

6 

2 

6, 

2 

7' 

5 

6 

4 

4 

2^ 

7 

4 

3 

4i 

3 

21 

2 

71 

5: 

8] 

61 

3^ 

2 

6J 

5 

8J 

8 

3J 

5 

6 

4j 

7 

1 

3 

Notice  t 

b  te 

n. 

he  groups  o 

f  figures 

whi 

ch  mak 

9.   7 

5 

4 

7 

2 

10. 

2 

3 

6 

4 

4 

3 

5 

0 

9 

6 

0 

4 

6 

7 

4 

4 

4 

3 

0 

3 

8 

5 

7 

3 

6 

5 

2 

2 

1 

5 

3 

5 

2 

2 

6 

5 

6 

7 

3 

4 

5 

8 

1 

0 

5 

2 

0 

3 

7 

1 

5 

6 

5 

8 

5 

9 

3 

6 

2 

8 

9 

1 

4 

9 

8 

0 

8 

1 

6 

6 

7 

7 

3 

9 

8 

6 

2 

6 

6 

4 

4 

3 

3 

1 

2 

1 

7 

4 

5 

1 

8 

2 

7 

6 

2 

WHOLE  NUMBERS      ADDITION 


13 


Add: 

1.  3 

2 

8 

4 

6 

2.  3 

5 

9 

7 

2 

1 

6 

7 

9 

4 

2 

3 

0 

8 

9 

9 

4 

4 

5 

5 

6 

6 

7 

7 

8 

5 

8 

4 

9 

3 

.2 

7 

8 

1 

4 

3.  6 

5 

8 

4 

2 

4.  3 

6 

8 

7 

5 

7 

1 

3 

2 

4 

5 

6 

8 

4 

6 

8 

5 

0 

6 

0 

7 

0 

8 

0 

5 

2 

3 

2 

9 

5 

6 

7 

4 

3 

7 

2 

3 

2 

5.  4 

3] 

2 

7 

6.  1 

4^ 

5 

1 

5 

7' 
7  J 

3 

6 

4 

6 

1 

1 

1 

31 

6^ 

5 

4 

3 

5 

11 

41 

8 

0 

7J 

4, 

1 

5 

9 

8 

9^ 

6j 

41 

9 

2 

4^ 

7 

81 

8] 

3 

8 

81 

6j 

8 

0 

0 

5 

2j 

0 

3 

71 

2J 

3 

8 

5 

6, 

0 

6 

2J 

5 

3, 

•  1] 

9 

7 

5. 

7 

91 

9 

51 

7! 

2 

9j 

5 

6 

3 

9 

lj 

5 

5] 

3j 

4 

.  3 

7] 

4 

6 

2 
4 

5 

3 

3 

2 

8 

4 

7 

B 
5 

3 

7.  5 

2 

5 

8 

8.  1 

3 

6 

4 

6 

3 

4 

7 

6 

6 

3 

0 

3 

2 

3 

5 

1 

5 

3 

5 

2 

4 

8 

8 

7 

0 

3 

3 

5 

7 

6 

6 

1 

2 

9 

8 

3 

6 

4 

0 

9 

3 

1 

4 

5 

1 

2 

7 

9 

3 

0 

3 

3 

2 

0 

1 

8 

0 

3 

6 

1 

9 

5 

4 

5 

7 

9 

4 

6 

5 

8 

9 

2 

3 

3 

9 

6 

9 

6 

3 

4 

1 

9 

2 

4 

3 

4 

2 

4 

2 

6 

8 

0 

1 

3 

4 

3 

8 

7 

8 

5 

5 

1 

7 

6 

6 

5 

7 

1 

8 

2 

5 

5 

14 

ADDITION 

DRILL 

FOR 

RAPIDITY 

Add 

l. 

4 

7 

8 

6 

5 

2. 

6 

8 

3 

9 

9 

7 

9  • 

5 

4 

6 

7 

7 

5 

6 

3 

3. 

5 

6 

8 

7' 

9 

4. 

6 

9 

5 

3 

4 

2 

4 

1 

6 

5 

7 

2 

4 

6 

8 

9 

3 

6 

5 

6 

4 

7 

6 

2 

5 

6. 

5 

2 

8 

4 

7 

6. 

9 

5 

6 

2 

3 

1 

9 

4 

5 

6 

7 

3 

3 

8 

2 

4 

3 

7 

1 

2 

5 

7 

1 

9 

8 

6 

8 

4 

5 

5 

2 

6 

8 

7 

3 

7. 

8 

4 

2 

7 

5 

8. 

4 

1 

9 

6 

3 

2 

5 

3 

8 

4 

2 

5 

1 

4 

6 

7 

9 

8 

3 

7 

6 

4 

3 

8 

5 

2 

9 

3 

8 

6 

5 

1 

9 

2 

7 

3 

6 

7 

4 

8 

5 

7 

4 

3 

2 

9. 

8 

5 

9 

4 

3 

10. 

2 

1 

5 

4 

7 

6 

4 

8 

9 

5 

8 

3 

4 

7 

1 

3 

2 

4 

1 

9 

6 

8 

3 

9 

7 

9 

8 

1 

6 

4 

2 

8 

6 

5 

8 

1 

7 

6 

4 

3 

5 

7 

3 

5 

2 

11. 

6 

5 

3 

4 

8 

12. 

1 

2 

7 

4 

9 

5 

8 

4 

1 

3 

9 

6 

6 

4 

2 

4 

3 

7 

8 

8 

5 

9 

2 

6 

6 

6 

3 

3 

5 

4 

5 

8 

1 

3 

7 

2 

9 

4 

6 

3 

4 

2 

7 

5 

8 

ADDITION       DRILL  FOR  RAPIDITY  15 


Add: 

1.   3 

7 

3 

8 

3 

2.   2 

7 

6 

3 

2 

2 

6 

7 

7 

6 

8 

6 

1 

2 

6 

0 

4 

4 

4 

8 

2 

5 

6 

0 

1 

7 

3 

2 

0 

0 

7 

3 

2 

1 

1 

5 

3 

8 

6 

9 

3 

2 

6 

8 

8 

5 

6 

2 

5 

9 

6 

8 

5 

9 

4 

4 

0 

3 

0 

4 

3 

0 

5 

7 

3 

1 

9 

3 

2 

4 

0 

9 

4 

5 

7 

8 

5 

1 

2 

1 

5 

4 

3 

9 

5 

Add  10  for  a 

group 

of  figures  equal  to  10. 

3.    2 

3 

2 

7 

4 

4.   2 

5 

2 

3 

1 

5 

7 

3 

6 

6 

4 

1 

8 

1 

4 

6 

5 

4 

3 

1 

8 

0 

4 

9 

5 

4 

1 

5 

9 

9 

4 

9 

4 

0 

8 

4 

7 

8 

8 

8 

6 

8 

6 

6 

3 

0 

5 

2 

0 

7 

3 

8 

5 

6 

3 

6 

0 

6 

2 

3 

9 

7 

3 

7 

5 

7 

9 

9 

5 

2 

5 

6 

0 

8 

7 

9 

1 

5 

5 

5 

7 

3 

2 

2 

3 

2 

5 

3 

3 

8 

3 

4 

7 

5 

2 

5.   6 

7 

5 

4 

6 

6.   3 

4 

3 

9 

2 

7 

2 

4 

5 

5 

7 

8 

8 

9 

5 

9 

3 

1 

6 

8 

5 

7 

5 

2 

3 

3 

9 

7 

4 

7 

6 

2 

8 

6 

4 

5 

5 

8 

9 

1 

3 

5 

2 

4 

4 

4 

8 

6 

9 

2 

1 

9 

5 

5 

7 

6 

7 

4 

3 

4 

9 

6 

9 

3 

8 

8 

3 

9 

7 

9 

8 

3 

4 

2 

3 

2 

5 

5 

8 

5 

5 

1 

6 

8 

2 

7 

6 

3 

6 

5 

4 

8 

3 

7 

5 

16 

ADDITION 

DRILL 

FOR  RAPIDITY 

Add: 

1.   2 

7 

9 

5 

6 

2.    3 

2 

9 

4 

7 

0 

3 

9 

2 

5 

5 

3 

3 

5 

5 

8 

4 

2 

0 

4 

4 

4 

7 

1 

8 

7 

2 

0 

3 

2 

0 

1 

4 

8 

3 

9 

4 

4 

6 

8 

7 

7 

4 

8 

3 

6 

0 

5 

9 

7 

6 

5 

8 

0 

4 

5 

6 

1 

5 

2 

9 

3 

6 

4 

2 

4 

6 

7 

2 

0 

5 

5 

3 

6 

7 

1 

3 

0 

1 

4 

1 

8 

7 

7 

1 

8 

7 

3 

7 

9 

8 

8 

2 

9 

5 

3.   3 

4 

8 

5 

6 

4.    1 

9 

3 

4 

7 

2 

7 

4 

6 

8 

0 

3 

3 

7 

5 

9 

3 

8 

0 

6 

4 

7 

2 

8 

8 

1 

3 

7 

4 

2 

9 

6 

7 

5 

4 

8 

0 

9 

9 

6 

5 

5 

4 

3 

2 

5 

7 

2 

1 

8 

6 

5 

6 

7 

9 

1 

5 

5 

2 

9 

4 

3 

8 

3 

7 

4 

6 

5 

7 

3 

8 

2 

9 

6 

1 

8 

4 

4 

2 

9 

3 

3 

0 

7 

2 

2 

5 

8 

4 

6 

5 

1 

5 

0 

8 

5.    3 

6 

1 

4 

2 

6.    8 

7 

9 

5 

3 

1 

8 

7 

6 

0 

5 

4 

4 

3 

7 

2 

1 

9 

3 

7 

2 

9 

4 

7 

7 

6 

1 

9 

8 

3 

7 

1 

0 

5 

8 

8 

7 

1 

5 

4 

1 

6 

6 

5 

5 

2 

9 

4 

5 

7 

2 

5 

8 

4 

2 

5 

6 

3 

8 

9 

6 

2 

3 

9 

4 

1 

8 

6 

5 

7 

2 

1 

5 

3 

4 

4 

0 

7 

2 

1 

2 

7 

5 

4 

8 

6 

2 

2 

7 

5 

8 

4 

2 

3 

1 

ADDITION      DRILL  FOR  RAPIDITY  17 


id: 
1.   2 

4 

6 

5 

8 

2.   7 

6 

1 

4 

2 

7 

8 

3 

9 

6 

5 

8 

9 

3 

7 

5 

1 

7 

4 

2 

4 

3 

9 

7 

2 

8 

9 

4 

6 

7 

6 

8 

3 

4 

1 

3 

2 

6 

5 

4 

9 

4 

5 

3 

3 

2 

7 

1 

3 

5 

2 

7 

4 

6 

7 

4 

8 

3 

5 

8 

1 

6 

3 

2 

2 

5 

4 

9 

0 

6 

7 

2 

7 

4 

3.   5        6        4        2        9  4.   8 


5.   5 


3   .     1 


2 

8 

5 

7 

4 

7 

5 

3 

2 

8 

6 

1 

9 

8 

5 

4 

2 

7 

9 

4 

8 

7 

6 

2 

3 

1 

9 

8 

4 

6 

6 

8 

4 

9 

6 

3 

8 

5 

5 

1 

3 

2 

1 

4 

6 

8 

1 

4 

6 

3 

7 

8 

5 

6 

2 

3 

5 

6 

2 

4 

6 

4 

3 

1 

8 

2 

3 

2 

8 

6 

2 

3 

9 

8 

5 

4 

7 

3 

1 

5 

3 

6 

4 

3 

2 

6 

2 

7 

4 

1 

5 

7 

8 

6 

9 

6.   4 

8 

6 

5 

3 

6 

9 

7 

4 

9 

6 

8 

3 

8 

9 

4 

7 

5 

9 

2 

8 

4 

7 

7 

8 

8 

5 

6 

5 

9 

7- 

4 

3 

6 

5 

7 

5 

3 

8 

5 

9 

6 

8 

4 

3 

2 

7 

5 

9 

3 

8 

7 

6 

9 

7 

6 

4 

8 

5 

7 

2 

5 

6 

5 

9 

9 

2 

3 

5 

8 

6 

8 

4 

6 

4 

5 

8 

5 

7 

5 

9 

6 

3 

8 

5 

2 

7 

2 

9 

3 

6 

9 

8 

4 

6 

1$                     WHOLE  NUMBERS  SUBTRACTION 

1.     4  less  2  2.    11  -  3  3.    12  -  4             4.    14  -  5 

7  less  2  9-3  5-4  7-5 

5  less  2  3-3  9-4  12-5 

8  less  2  5-3  6-4  8-5 
3  less  2  7-3  8-4  5-5 
2  less  2  6-3  10-4.  6-5 

9  less  2  4-3  4-4  9-5 

6  less  2  8-3  7-4  10-5 

10  less  2  10-3  11-4  11-5 

11  less  2  12-3  13-4  13-5 


Subtract : 


5. 

24 

37 

85 

69 

46 

21 

72 

33 

68 

50 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

6. 

54 

67 

55 

49 

76 

31 

92 

83 

58 

70 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

7. 

44 

27 

65 

59 

56 

51 

82 

43 

28 

60 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

8. 

94 

87 

25 

89 

36 

41 

62 

53 

78 

80 

5 

5 

5 

5 

5 

5 

5 

5 

5 

_5 

9. 

80 

87 

82 

85 

88 

83 

89 

86 

81 

84 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

10. 

63 

60 

69 

66 

67 

65 

61 

68 

62 

64 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

11. 

55 

58 

51 

54 

59 

57 

53 

56 

50 

52 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

12. 

32 

36 

35 

39 

30 

38 

34 

37 

31 

33 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

WHOLE   NUMBERS       SUBTRACTION  19 

1.    14  less  6  2.    15  -  7  3.    17  minus  8          4.     9  -  9 

9  less  6  10-7  11  minus  8  12-9 

11  less  6  7-7  16  minus  8  18-9 
10  less  6  14-7  12  minus  8  10-9 

8  less  6  9-7  9  minus  8  15-9 

7  less  6  11-7  13  minus  8  11-9 

12  less  6  13-7  14  minus  8  14-9 
6  less  6  16-7  10  minus  8  16-9 

13  less  6  8-7  8  minus  8  13-9 
15  less  6  12-7  15  minus  8  17-9 


Subtract : 


5. 

24 

37 

85 

69 

46 

21 

72 

33 

68 

50 

6 

6 

6 

_6 

_6 

6 

6 

6 

6 

6 

6. 

54 

67 

55 

49 

76 

31 

92 

83 

58 

70 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7. 

44 

27 

65 

59 

56 

51 

82 

43 

28 

60 

8 

8 

8 

8 

_8 

8 

8 

8 

8 

8 

8. 

94 

87 

25 

89 

36 

41 

62 

53 

78 

80 

9 

9 

9 

9 

9 

9 

9 

_9 

9 

9 

9.  46   44   49   43   40   42   47   45   41    48 
16   16   16   16   16    16    16    16    16    16 


10. 

74 

70 

79 

72 

76 

78 

75 

71 

77 

73 

17 

J7 

17 

17 

17 

17 

17 

17 

17 

17 

11. 

23 

26 

29 

20 

24 

28 

21 

27 

22 

25 

18 

18 

18 

18 

18 

18 

18 

JL8 

_18 

18 

12. 

96 

92 

99 

95 

90 

98 

94 

91 

93 

97 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

20 


WHOLE  NUMBERS       SUBTRACTION 


1. 

8 

9 

11 

17 

10 

15 

12 

9 

14 

7 

2 

3 

4 

8 

6 

5 

3 

5 

3 

2 

2. 

16 

10 

18 

12 

19 

8 

11 

14 

15 

8 

5 

4 

7 

5 

3 

5 

2 

6 

4 

4 

3. 

14 

12 

13 

10 

16 

15 

14 

11 

13 

18 

7 

7 

6 

5 

9 

6 

_8 

5 

2 

3 

4. 

11 

15 

19 

10 

12 

18 

16 

13 

17 

14 

10 

10 

10 

10 

10 

10 

10 

10 

10 

JO 

Think  of  9  as 

10  less  1. 

Think  of  1 

1  as 

10  plus  1 

5.  32- 

-9 

6. 

55-9 

7. 

72-  1 

8.  45- 

-  11 

36- 

-9 

51-9 

76-  1 

41  - 

-  11 

33- 

-9 

54-9 

73-  1 

44- 

-  11 

39- 

-9 

58-9 

79-  i: 

48- 

-  11 

35- 

-9 

52-9 

75  -  i; 

42- 

-  11 

30- 

-9 

50-9 

70-  1] 

47- 

11 

34- 

-9 

57-9 

74-  1] 

40- 

-  11 

37- 

-9 

53-9 

77-  1] 

43- 

-  11 

31  - 

-9 

56-9 

71  -  1] 

46- 

11 

38- 

-9 

59-9 

78-  1] 

49- 

11 

Subtract : 

9.  45 

38 

86 

72 

55 

77 

94 

65 

89 

54 

31. 

24 

55 

30 

14 

46 

71 

23 

_?z 

32 

10.  29 

37 

48 

56 

65 

74 

89 

98 

66 

57 

22 

16 

27 

34 

42 

51 

75 

26 

35 

46 

11.  35 

54 

63 

82 

76 

90 

43 

51 

64 

72 

28 

45 

45 

36 

48 

27 

26 

33 

45 

54 

12.  70 

40 

30 

80 

90 

60 

50 

70 

80 

60 

35 

24 

16 

52 

67 

38 

21 

49 

33 

_26 

WHOLE  NUMBERS      SUBTRACTION  21 

Drill  for  Rapidity. 


1.   12-4 

4.   87-9 

7.    76-4 

10.   33  -  5 

33-2 

13-7 

88-7 

61-3 

26-3 

72-2 

15-2 

95-6 

40-7 

63-4 

32-5 

56-9 

58-9 

41-5 

94-8 

20-3 

62-6 

36-7 

78-3 

83-4 

19-5 

98-6 

25-6 

74-6 

64-2 

27-3 

47-4 

36-2 

96-8 

95-9 

81-3 

71-5 

71-4 

57-7 

48-8 

92-9 

2.   24-9 

6.   65-4 

8.   70-7 

11.   63-2 

55-8 

17-8 

93-9 

40-4 

89-5 

30-2 

54-3 

35-5 

35-6 

66-8 

11-7 

68-7 

73-3 

72-5 

38-5 

17-8 

29-7 

31-9 

74-2 

96-4 

60-5 

45-5 

21-6 

52-3 

44-4 

97-6 

43-7 

34-  10 

83-6 

18-7 

84-5 

80-6 

50-8 

56-4 

46-7 

15-7 

3.    16-6 

6.   69-2 

9.   91-8 

12.   78-5 

39-9 

37-5 

79-3 

44-9 

86-5 

80-6 

28-4 

55-3 

99-4 

92-7 

49-8 

39-4 

20-9 

23-8 

53-4 

72-  10 

61-2 

68-2 

77-2 

41-5 

52-8 

42-7 

51-5 

54-6 

67-3 

34-3 

85-3 

93-9 

22-5 

82-4 

59-6 

65-6 

90-3 

75-7 

14-9 

24-7 

22  WHOLE  NUMBERS       SUBTRACTION 

Practice  first  for  accuracy,  then  for  speed. 

1.  Starting  at  24  subtract  2's  until  but  2  is  left. 

2.  Starting  at  36  subtract  3's  until  but  3  is  left. 

3.  Starting  at  48  subtract  4's  until  but  4  is  left. 

4.  Starting  at  60  subtract  5's  until  but  5  is  left. 

5.  Starting  at  72  subtract  6's  until  but  6  is  left. 

6.  Starting  at  84  subtract  7's  until  nothing  is  left. 

7.  Starting  at  96  subtract  8's  until  nothing  is  left. 

8.  Starting  at  108  subtract  9's  until  nothing  is  left. 

9.  Starting  at  120  subtract  10's  until  nothing  is  left. 
10.  Starting  at  132  subtract  11 's  until  nothing  is  left. 


1.  Starting  at  50  subtract  2's  until  you  reach  zero. 

2.  Starting  at  60  subtract  3's  until  you  reach  zero. 

3.  Starting  at  80  subtract  4's  until  you  reach  zero. 

4.  Starting  at  100  subtract  5's  until  you  reach  zero. 

5.  Starting  at  102  subtract  6's  until  you  reach  zero. 

6.  Starting  at  105  subtract  7's  until  you  reach  zero. 

7.  Starting  at  104  subtract  8's  until  you  reach  zero. 

8.  Starting  at  200  subtract  10's  until  you  reach  zero. 


1.  Starting  at  100  subtract  3  as  many  times  as  you  can. 

2.  Starting  at  100  subtract  6  as  many  times  as  you  can. 

3.  Starting  at  100  subtract  7  as  many  times  as  you  can. 

4.  Starting  at  100  subtract  8  as  many  times  as  you  can. 

5.  Starting  at  100  subtract  9  as  many  times  as  you  can. 

6.  Starting  at  100  subtract  11  as  many  times  as  you  can. 

7.  Starting  at  100  subtract  12  as  many  times  as  you  can. 

8.  Starting  at  90  subtract  4  as  many  times  as  you  can. 

9.  Starting  at  99  subtract  5  as  many  times  as  you  can. 


1. 


2. 


ADDITION  AND   SUBTRACTION  23 

Drill  for  Rapidity. 


5  +  2 

4.     7-2 

7.   3  +  4 

10.    14-6 

7  +  3 

6-3 

7  +  5 

16-9 

9  +  5 

10-4 

8  +  3 

12-7 

6  +  6 

9-5 

6  +  2 

13-6 

4  +  8 

11-9 

5  +  8 

6-2 

2  +  9 

12-8 

4  +  9 

8-4 

8  +  4 

10-7 

3  +  6 

13-5 

5  +  5 

12-6 

5  +  7 

9-3 

8  +  7 

9-4 

6  +  4 

11-6 

5  +  6 

11-5 

9  +  2 

5-2 

9  +  9 

5.    11-8 

8.   4  +  5 

11.    14-7 

2  +  4 

15-9 

3  +  3 

8-3 

6  +  3 

7-6 

9  +  8 

17-8 

7  +  8 

8-5 

6  +  7 

7-4 

3  +  9 

9-2 

5  +  9 

14-9 

8  +  6 

7-3 

7  +  6 

7-5 

3  +  2 

12-9 

4  +  2 

8-6 

5  +  3 

14-8 

5  +  4 

13-8 

9  +  4 

11-7 

8  +  5 

18-9 

2  +  7 

10-6 

4  +  3 

15-7 

6  +  9 

6.    12-5 

9.   8  +  8 

12.    12-4 

7  +  7 

11-3 

7  +  9 

11-2 

8  +  2 

8-2 

3  +  7 

14-5 

9  +  3 

9-6 

9  +  6 

5-3 

4  +  4 

16-8 

7  +  4 

15-8 

6  +  5 

13-7 

2  +  5 

13-4 

2  +  6 

10-2 

6  +  6 

10-3 

4  +  7 

12-3 

9  +  7 

11-4 

8  +  9 

6-4 

3  +  8 

13-9 

7  +  2 

10-5 

6  +  8 

15-6 

24  ADDITION  AND  SUBTRACTION 

Add,  and  subtract : 


1.  40 

60 

80 

70 

90 

20 

30 

50 

30 

20 

10 

50 

60 

10 

20 

20 

2.  60 

50 

70 

40 

80 

30 

90 

70 

30 

40 

70 

20 

60 

10 

50 

40 

3.  90 

80 

60 

50 

70 

40 

80 

60 

30 

50 

10 

30 

20 

10 

30 

40 

4.  90 

80 

70 

60 

90 

80 

70 

90 

40 

40 

30 

50 

20 

20 

60 

70 

5. 

110 

90 

120 

80 

170 
70 

150 
60 

140 
50 

180 
40 

160 
30 

190 
20 

6. 

260 
20 

210 
30 

240 
40 

290 
50 

220 
60 

270 

80 

230 
70 

250 
90 

7. 

350 
20 

320 
70 

390 
40 

360 
80 

330 
60 

380 
50 

340 
90 

370 
30 

8. 

520 
30 

640 
50 

720 
90 

840 
50 

750 
70 

930 
40 

630 

80 

410 
60 

9. 

260 

540 

360 

750 

420 

350 

300 

600 

110 

420 

240 

500 

120 

220 

150 

250 

10. 

320 

310 

400 

560 

220 

800 

240 

250 

200 

160 

380 

480 

190 

250 

180 

160 

11. 

280 

200 

300 

400 

500 

600 

700 

800 

140 

130 

210 

280 

340 

480 

150 

^20 

12. 

290 

660 

430 

590 

810 

550 

350 

750 

150 

200 

100 

300 

600 

150 

250 

350 

ADDITION  AND   SUBTRACTION  25 

1.  Count  by  2's  to  20,  and  back  by  2's  to  2. 

2.  Count  by  3's  to  30,  and  back  by  3's  to  3. 

3.  Count  by  4's  to  40,  and  back  by  4's  to  4. 

4.  Count  by  5's  to  50,  and  back  by  5's  to  5. 

5.  Count  by  6's  to  60,  and  back  by  6's  to  6. 

6.  Count  by  7's  to  70,  and  back  by  7's  to  7. 

7.  Count  by  8's  to  80,  and  back  by  8's  to  8. 

8.  Count  by  9's  to  90,  and  back  by  9's  to  9. 


9.  Count  by  3's  to  60.     Count  back  to  3. 

10.  Count  by  4's  to  80.     Count  back  to  4. 

11.  Count  by  6's  to  120.     Count  back  to  6. 

12.  Count  by  7's  to  140.     Count  back  to  7. 

13.  Count  by  8's  to  160.     Count  back  to  8. 

14.  Count  by  9's  to  180.     Count  back  to  9. 

15.  Count  by  ll's  to  220.     Count  back  to  11. 

16.  Count  by  12's  to  240.     Count  back  to  12. 


169? 
l  225? 


17.  Count  by  13's  to  169.     How  many  13's  in 

18.  Count  by  15's  to  225.     How  many  15's  in  225? 

19.  Count  by  16's  to  256.     How  many  16's  in  256? 

20.  Count  by  20's  to  400.     How  many  20's  in  400? 

21.  Count  by  25's  to  625.     How  many  25's  in  625? 

22.  What  is  meant  by  the  " square"  of  a  number? 

23.  What  is  the  square  of  13?    Of  15?    Of  16?    Of20?Of25? 


26 


WHOLE  NUMBERS      MULTIPLICATION 


3. 


5  times  2  =  ? 
9  times  2  .=  ? 
2  times  2  =  ? 

How  many  2's  in  18? 
How  many  2's  in  10  ? 
How  many  2's  in  6? 
How  many  2's  in  24  ? 
How  many  2's  in  12  ? 

10  20  30 

X2         X2         X2 


Count  by  2's  to  24,  and  back  to  2 
Recite  the  table  of  2's. 

7x2=?  10  times  2 

1X2-  ? 
4X2=  ? 


40 
X2 


3  times  2  =  ? 
12  times  2  =  ? 

How  many  2's  in  22? 
How  many  2's  in  8? 
How  many  2's  in  16? 
How  many  2's  in  4  ? 
How  many  2's  in  14? 

50  60  70 

X2  X2  X2 


6X2  = 
11  X2  = 

8x2  = 


80 

X2 


90 

X2 


)ly: 

Multii 

4. 

11 

21 

31 

41 

51 

61 

71 

81 

91 

2 

2 

2 

2 

2 

2 

2 

2 

2 

5. 

12 

22 

32 

42 

52 

62 

72 

82 

92 

2 

2 

2 

2 

2 

2 

2 

2 

2 

6. 

13 

23 

33 

43 

53 

63 

73 

83 

93 

2 

2 

2 

2 

2 

2 

2 

2 

2 

7. 

14 

24 

34 

44 

54 

64 

74 

84 

94 

2 

2 

2 

2 

2 

2 

_2^ 

2 

2 

8. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

2 

2 

2 

2 

2 

2 

.   2 

2 

2 

9. 

16 

2 

2 

2 

2 

2 

2 

2 

2 

2 

10. 

17 

27 

37 

47 

57 

67 

77 

87 

97 

2 

2 

2 

2 

2 

2 

2 

2 

2 

11. 

18 

28 

38 

48 

58 

68 

78 

88 

98 

2 

2 

2 

2 

2 

2 

2 

2 

2 

12. 

19 

29 

39 

49 

59 

69 

79 

89 

99 

2 

2 

2 

2 

2 

2 

2 

2 

2 

WHOLE  NUMBERS     MULTIPLICATION 


27 


8x3=? 

1  X3=  ? 

12  x  3  =  ? 


Count  by  3's  to  36,  and  back  to  3. 
Recite  the  table  of  3's. 

1.  3x3=?       8x3=?       7x3=? 
10  X  3  =  ? 

5X3=? 

2.  How  many  3's  in  12? 
How  many  3's  in  21  ? 
How  many  3's  in  9? 
How  many  3's  in  24? 
How  many  3's  in  15? 

3.  10  20  30  40  50 

X3         X3         X3  X3  X3 


6x3  = 


4x3=?  2x3 

11X3=?  9x3=? 

How  many  3's  in  6? 
How  many  3's  in  18? 
How  many  3's  in  36? 
How  many  3's  in  33? 
How  many  3's  in  27? 

60  70        80  90 

X3         X3        X3        X3 


)ly: 
11 

81 

iltii 
4. 

21 

31 

41 

51 

61 

71 

91 

3 

3 

3 

3 

3 

3 

3 

_3 

3 

5. 

12 

22 

32 

42 

52 

62 

72 

82 

92 

3 

3 

3 

_3 

3 

3 

3 

_3 

3 

6. 

13 

23 

33 

43 

53 

63 

73 

83 

93 

3 

3 

3 

3 

3 

3 

3 

3 

_3 

7. 

.14 

24 

34 

44 

54 

64 

74 

84 

94 

3 

3 

3 

3 

3 

3 

3 

3 

_3 

8. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

3 

3 

3 

3 

3 

3 

3 

3 

_3 

9. 

16 

26 

36 

46 

56 

66 

76 

86 

96 

3 

3 

3 

_3 

^3 

_3^ 

3 

3 

3 

10. 

17 

27 

37 

47 

57 

67 

77 

87 

97 

3 

3 

_3 

3 

3 

3 

3 

3 

3 

11. 

18 

28 

38 

48 

58 

68 

78 

88 

98 

3 

3 

3 

3 

_3^ 

3 

3  ' 

_3^ 

3 

12. 

19 

29 

39 

49 

59 

69 

79 

89 

99 

3 

3 

3 

3 

3 

3 

3 

_3 

3 

28                 WHOLE  NUMBERS  MULTIPLICATION 

Count  by  4's  to  48,  and  back  to  4. 
Recite  the  table  of  4's. 

1.  5x4=?                6x4=?  1x4=?                   3x4=? 
8X4=?                 2x4=?  7X4=?                  10x4=? 

11X4=?               12x4=?  9x4=?                    4x4=? 

2.  36  is  how  many  times  4?  16  is  how  many  times  4? 
12  is  how  many  times  4?  8  is  how  many  times  4? 
28  is  how  many  times  4?  24  is  how  many  times  4? 
20  is  how  many  times  4  ?  48  is  how  many  times  4  ? 
44  is  how  many  times  4  ?  32  is  how  many  times  4  ? 

3.  10           20           30           40  50           60           70         80          90 

X4          X4          X4          X4  X4          X4          X4        X4         X4 

Multiply : 


4.  11 

21 

31 

41 

51 

61 

71 

81 

91 

4 

4 

4 

4 

4 

4 

4 

4 

4 

5.  12 

22 

32 

42 

52 

62 

72 

82 

92 

4 

4 

4 

4 

4 

4 

4 

4 

4 

6.  13 

23 

33 

43 

53 

63 

73 

83 

93 

4 

4 

4 

4 

4 

4 

4 

4 

4 

7.  14 

24 

34 

44 

54 

64 

74 

84 

94 

4 

4 

4 

4 

_^ 

_4^ 

4 

4 

_J 

8.  15 

25 

35 

45 

55 

65 

75 

85 

95 

4 

4 

4 

4 

4 

4 

4 

4 

4 

9. 

16 

26 

36 

46 

56 

66 

76 

86 

96 

4 

4 

4 

4 

4 

4 

4 

4 

_J 

10. 

17 

27 

37 

47 

57 

67 

77 

87 

97 

_^ 

4 

4 

4 

4 

4 

4 

4 

4 

11. 

18 

28 

38 

48 

58 

68 

•  78 

88 

98 

4 

4 

4 

4 

4 

4 

4 

4 

4 

12. 

19 

29 

39 

49 

59 

69 

79 

89 

99 

_^ 

4 

4 

4 

4 

4 

4 

4 

4 

WHOLE  NUMBERS      MULTIPLICATION  29 

Count  by  5's  to  60,  and  back  to  5. 
Recite  the  table  of  5's. 

1.  12x5=?  9x5=?  4x5=?  2x5=? 

3X5=?  11X5=?  6x5=?  5x5=? 

8X5=?  7X5=?  10x5=?  1x5=? 

2.  25  is  how  many  times  5  ?  55  is  how  many  times  5  ? 
40  is  how  many  times  5  ?  20  is  how  many  times  5  ? 
15  is  how  many  times  5?  45  is  how  many  times  5? 
60  is  how  many  times  5?  30  is  how  many  times  5? 
35  is  how  many  times  5?  10  is  how  many  times  5? 

3.  10  20  30  40  50  60  70  80  90 

X5         X5         X5         X5         X5  X_5         X_5         X5         X_5 

Multiply : 


4.  11 

21 

31 

41 

51 

61 

71 

81 

91 

5 

_J> 

5 

_5 

_5 

J> 

_5 

_5 

_5 

5.  12 

22 

32 

42 

52 

62 

72 

82 

92 

_5 

5 

_5 

5 

5 

_5 

5 

5 

5 

6.  13 

23 

33 

43 

53 

63 

73 

83 

93 

5 

_5 

5 

J> 

_5 

_5 

_5 

5 

_5 

7.  14 

24 

34 

44 

54 

64 

74 

84 

94 

5 

_5 

5 

_5 

_5 

_5 

_5 

_5 

_5 

8. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

_5 

_5 

5 

^5 

_5 

_5 

j5 

_5 

5 

9. 

16 

26 

36 

46 

56 

66 

76 

86 

96 

_5 

_5 

J5 

5 

_5 

_5 

5 

j5 

5 

10. 

17 

27 

37 

47 

57 

67 

77 

87 

97 

_5 

_5 

_5 

_5 

_^ 

_5 

_5 

5 

5 

11. 

18 

28 

38 

48 

58 

68 

78 

88 

98 

_5 

_5 

_5 

5 

_5 

J5 

_5^ 

_5^ 

_5 

12. 

19 

29 

39 

49 

59 

69 

79 

89 

99 

■_ft 

5 

5 

Jy 

_5 

_5 

5 

^5 

_5 

30  WHOLE  NUMBERS      MULTIPLICATION 

Count  by  6's  to  72,  and  back  to  6. 
Recite  the  table  of  6's.     Recite  it  backwards. 

1.  6x6=?  5x6=?  1x6=?  3x6=? 
10x6=?                12x6=?                4x6=?  9x6=? 

2x6=?  8x6=?  11x6=?  7x6=? 

How  many  6's 

2.  In  54?  In  72?  In  42?  In  48?  In  66? 
In  30?                In  12?                In  18?                In  36?  In  24? 

3.  10  20  30  40  50  60  70  80  90 

X6         X6         X6  X6  X6         x6         X6         x6  x6 


4.    11  X  5 

5.    12x5 

6.      3X4 

7.      2x2 

5X4 

10x2 

8x2 

4X3 

12x3 

5X5 

9X5 

8X5 

6x2 

11  X  3 

10x4 

6x4 

11  X  4 

7x2 

9X3 

7x3 

5x3 

9X4 

11  X  2 

9x2 

4x2 

10X3 

12x4 

2x4 

8X3 

7x4 

3x3 

10X5 

7X5 

3x5 

4x4 

12x2 

6X3 

8x4 

6x5 

2x3 

2x5 

3X2 

5X2 

4x5 

Multiply : 


8. 

11 

21 

31 

41 

51 

61 

71 

81 

91 

6 

_6 

6 

6 

6 

6 

6 

6 

6 

9. 

12 

22 

32 

42 

52 

62 

72 

82 

92 

_6 

_6 

_6 

6 

_6 

_6 

6 

6 

6 

10. 

13 

23 

33 

43 

53 

63 

73 

83 

93 

_6 

6 

6 

6 

6 

6 

6 

6 

6 

11. 

14 

24 

34 

44 

54 

64 

74 

84 

94 

6 

_6 

_6 

6 

J> 

6 

6 

6 

_6 

12. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

_6 

_6 

_6 

6 

_6 

6 

6 

6 

6 

WHOLE  NUMBERS      MULTIPLICATION  31 

Count  by  7's  to  84,  and  back  to  7. 
Recite  the  table  of  7's.     Recite  it  backwards. 

1.  7X7=?                   2x7=?                5X7=?  4x7=? 
12x7=?                  8x7=?                1x7=?  6x7=? 

3x7=?                11x7=?              10x7=?  9x7=? 

How  many  7's 

2.  In  14?               In  84?               In  49?               In  42?  In  35? 
In  28?               In  21?               In  77?               In  63?  In  56? 

3.  10           20           30           40           50           60           70  80           90 

X7          X7          X7         X7         X7          X7          X7  X7          X7 


12x3 

5.    11x5 

6.      6x5 

7.      6x6 

9x4 

10X3 

12x4 

5x5 

2x5 

8x4 

9x3 

3X4 

8x6 

5X6 

4x6 

8x3 

5X3 

4x5 

3x5 

9x5 

10x6 

11  X  3 

3x3 

12x6 

12x5 

6x3 

6X4 

5X4 

11  X  4 

10X5 

7X6 

4x3 

7x3 

11  X  6 

2x4 

9x6 

4x4 

8x5 

2x6 

10X4 

2x3 

7x4 

7x5 

3X6 

Multiply : 


8. 

11 

21 

31 

41 

51 

61 

71 

81 

91 

7 

_7_ 

7 

7 

7 

7 

7 

7 

_J_ 

9. 

12 

22 

32 

42 

52 

62 

72 

82 

92 

7 

7 

_7_ 

7 

7 

7 

7 

7 

J7 

10. 

13 

23 

33 

43 

53 

63 

73 

83 

93 

7 

_7 

_7 

_7 

_J7 

J_ 

7 

7 

_7 

11. 

14 

24 

34 

44 

54 

64 

74  " 

84 

94 

7 

_7 

7 

J_ 

_7 

_7 

J_ 

7( 

7 

12. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

7 

7 

7 

7 

7 

7 

Jl 

7 

7 

32                  WHOLE  NUMBERS  MULTIPLICATION 

Count  by  8's  to  96,  and  back  to  8. 

Recite  the  table  of  8's.  Recite  it  backwards. 

1.  6x8=?  2x8=?  4X8=?  8x8=? 
3X8=?  10x8=?  12x8=?  11x8=? 
9x8=?                  7X8=?  5X8=?  1x8=? 

2.  8  X  ?  =  16.  8  X  ?  =  24.  8  X  ?  =  32.  8  X  ?  =  48. 
8  X  ?  =  40.  8  X  ?  =  80.  8  X  ?  =  64.  8  X  ?  =  72. 
8  X  ?  =  96.             8  X  ?  =  56.  8  X  ?  =  88.  8  X  ?  =  8. 

3.  10           20           30           40  50           60           70  80           90 

X8         X8          X8         X8  X8          X8          X8  X8          X8 


4.     5x4 

5.    11  X  4 

6.     2x6 

7.     3x7 

7X5 

7x7 

3x5 

7X6 

8X6 

5x6 

8x7 

8x4 

10x7 

4x5 

3x4 

12x6 

11  X  5 

3X6 

10X6 

5X7 

9x4 

6X4 

9X7 

9x6 

4X7 

11  X  7 

2x5 

10X5 

6x6 

9x5 

4X6 

2x7 

7x4 

6x7 

4x4 

6x5 

12x5 

12x4 

8X5 

12x7 

2x4 

10x4 

11  X  6 

5X5 

Multiply : 


8. 

11 

21 

31 

41 

51 

61 

71 

81 

91 

_8 

_8 

8 

8 

8 

8 

8 

_8 

_8 

9. 

12 

22 

32 

42 

52 

62 

72 

82 

92 

_8 

_8 

8 

8 

8 

8 

_8 

8 

_§• 

10. 

13 

23 

33 

43 

53 

63 

73 

83 

93 

8  . 

_8 

8 

8 

8 

_8 

8 

8 

_8 

11. 

14 

24 

34 

44 

54 

64 

74 

84 

94 

_8 

_8 

8 

8 

8 

_8 

_8 

8 

8 

12. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

8 

_8 

__8 

8 

8 

8 

8 

8 

_8 

WHOLE  NUMBERS      MULTIPLICATION  33 

Count  by  9's  to  108,  and  back  to  9. 
Recite  the  table  of  9's.     Recite  it  backwards. 

1.  9X9=?                5X9=?              8X9=?  11x9=? 
3x9=?              12x9=?               1x9=?  2x9=? 

10x9=?                4x9=?              7x9=?  6x9=? 

2.  9  X  ?  =  27              9  X  ?  =  81.             9  X  ?  =  18.  9  X  ?  =  90. 
9  X  ?  =  45.             9  X  ?  =  108.           9  X  ?  =  36.  9  X  ?  =  9. 
9  X  ?  =  63.             9  X  ?  =  72.             9  X  ?  =  54.  9  X  ?  =  99. 

3.  10           20           30           40           50           60           70  80           90 

X9         X9         X9         X9          X9          X9          x9  X9          X9 


9X5 

5.    12x8 

6.    8X6 

7.    12  x  7 

10  X  6 

9x6 

7X8 

11  X  5 

9X7 

10X5 

2x7 

8X7 

5x8 

5x6 

3X5 

4x8 

7x7 

.4X7 

7x6 

6X5 

4x6 

2x6 

8x5 

12x6 

2x8 

7x5 

6x8 

10x8 

5X5 

11  X8 

3x7 

5X7 

11  X  6 

6x6 

4x5 

10x7 

6x7 

12x5 

3x6 

2x5 

11  X  7 

8x8 

9x8 

3X8 

Multiply : 


8. 

11 

21 

31 

41 

51 

61 

71 

81 

91 

9 

_9 

9 

9 

9 

_9 

_9 

9 

_9 

9. 

12 

22 

32 

42 

52 

62 

72 

82 

92 

9 

9 

9 

9 

_9 

_9 

9 

9 

9 

10. 

13 

23 

33 

43 

53 

63 

73 

83 

93 

9 

9 

_9 

__9 

9 

_9 

_9 

_9 

_9 

11. 

14 

24 

34 

44 

54 

64 

74 

84 

94 

_9 

9 

9 

_9 

9 

_9 

_9 

_9 

_9 

12. 

15 

25 

35 

45 

55 

65 

75 

85 

95 

9 

_9 

_9 

9 

9 

_9 

_9 

_9 

9 

34  WHOLE   NUMBERS      MULTIPLICATION 

Count  by  12's  to  144,  and  back  to  12. 
Recite  the  table  of  12's.     Recite  it  backwards. 

1.      5  X  12  =  ?  6  X  12  =  ?      2.    12  X  ?  =  120.        12  X  ?  =  60. 


9X  12 

=  ? 

3X  12  = 

? 

12  X 

?    o 

-48. 

12 

X  ?  =  24. 

12  X  12 

=  ? 

10  X  12  = 

? 

12  X 

?  . 

=  72. 

12 

X  ?  =  96. 

4X  12 

=  ? 

7X12  = 

? 

12  X 

?  = 

=  108. 

12 

X  ?  =  120. 

8X  12 

=  ? 

11  X  12  = 

? 

12  X 

?    m 

=  36. 

12 

X  ?  =  84. 

2X12 

m  f 

1X12  = 

? 

12  X 

f    = 

132. 

12 

X  ?  =  12. 

3. 

10  X  11 

m    ? 

11  X 

11 

=  ? 

12  X  11  = 

,  f 

4. 

2x6 

5. 

7X  12 

6. 

3x6 

7. 

2x8 

8.    11  X  11 

9x9 

9X6 

4x7 

3x9 

9X8 

10X11 

5x9 

4x9 

7X7 

8x7 

12x7 

4x12 

5X  12 

4x6 

3x8 

6X6 

12x11 

8x9 

12x8 

2x9 

5x8 

9x7 

11  X  7 

11  X12 

8X  12 

11  X  9 

8x6 

5x6 

7x9 

10x9 

3X  12 

6x9 

12  x  12 

6X  12 

6x8 

2x7 

2x  12 

7x8 

3x7 

12x9 

8x8 

5X7 

6x7 

7x6 

4x8 

12x6 

11  X  6 

9X12 

11  X  8 

10  X  12 

Multiply : 

9. 

16 

26 

36           46 

56 

66 

76 

86          96 

6 

6 

6             6 

6 

6 

_6 

_6            6 

10. 

17 

27 

37           47 

57 

67 

77 

87          97 

_6 

6 

6          _6 

_6 

__6 

6 

_6          J5 

11. 

18 

28 

38           48 

58 

68 

78 

88          98 

_6 

_6 

6             6 

_6 

6 

_6 

_6             6 

12. 

19 

29 

39           49 

59 

69 

79 

89           99 

6 

_6 

_6          j6 

6 

_6 

_6 

6             6 

WHOLE  NUMBERS      MULTIPLICATION  35 

1.  2x2x2  2.  4x5x3  3.  10x2x5 

3x3x3  3x5x4  2x4x11 

2x4x8  4x4x4  8x5x2 

3x3x9  5x5x5  10x1x5 

5x2x5  5x3x2  2x2x7 

4x3x4  4x2x7  2x4x9 

2x3x9  2x6x6  3x3x7 

4x3x8  3x2x7  2x5x10 

6x2x7  3x4x3  5x5x3 

2x5x4  5x3x3  10x3x2 


10  X20 

5.  20  X  20 

6.  200  x  3 

11  X  20 

25x20 

500x6 

12  X  20 

30x20 

300x4 

13  X  20 

30x30 

400  x  5 

14  X  20 

40x20 

800x2 

15  X  20 

40  x  30 

600x8 

16x20 

50  x  20 

150x5 

17  x  20 

50x40 

250x4 

18x20 

40x40 

125x3 

19x20 

50x50 

450x2 

7.  16 

26 

36 

46 

56 

66 

76 

86 

96 

7 

7 

_7 

7 

7 

_7_ 

7 

7 

_7 

8.  17 

27 

37 

47 

57 

67 

77 

87 

97 

.  7 

7 

_1_ 

7 

7 

_J_ 

7 

7 

7 

9.  18 

28 

38 

48 

58 

68 

78 

88 

98 

7 

7 

_J_ 

7 

7 

7 

7 

7 

7 

.0.  19 

29 

39 

49 

59 

69 

79 

89 

99 

7 

7 

7 

7 

7 

7 

7 

7 

7 

36 


MULTIPLICATION    TABLES    REVERSED 


1.  20 
48 
16 
24 
12 
36 
28 
40 
32 
8 
44 

4.  10] 
60 
25 
40 
30 

•  15 
55 
20 
45 
50 
35 

7.  42] 
56 
14 
35 
84 
21 
70 
28 
49 
63 
77 


2.     56 

3.  12' 

32 

20 

72 

4 

16 

22 

How  many 
4's? 

40 
88 
24 
48 
64 
80 
96, 

5.     96 

24 

60 

120 

How 

|       8' 

many 

s? 

18 
8 
10 
6 
14 
24 
16, 

6.  15 

36 

6 

21 

How  many 
2'sf 

How  many 

36 

72 

How 

many 

9 
33 

How  many 

5's? 

108 

48 
144 

84 

132  ; 

8.     99 ' 
18 
45 
63 

12 

's? 

18 
27 
12 
24 
30. 

9.  24 
60 
12 
36 

3's? 

How  many 

7's? 

108 
36 
90 

27 
72 
54 
81 

How 
'       9' 

many 

s? 

66 
30 
72 

54 
42 

18 
48 

How  many 
6's? 

THE    FACTS    OF    THE    MULTIPLICATION    TABLES       37 
Drill  for  Rapidity. 


3. 


2x9 

4.  12  x  2 

7.  3  x  12 

10.  4x2 

5x  10 

5x4 

10x9 

3x9 

9x4 

6x6 

5X11 

11x3 

11x5 

11x8 

6x  10 

9x  10 

10x3 

2x  10 

5x2 

5x8 

6x2 

11  X  12 

8x3 

3x6 

9x8 

7x3 

10x7 

7x5 

4x  12 

8x5 

4x8 

10x4 

3x  11 

7x7 

2x6 

4x7 

5x6 

4x9 

12x4 

10  x  11 

3x7 

5.  2x11 

8.  9x5 

11.  9x12 

8x  12 

12  x  12 

12x9 

4x3 

6x3 

7x2 

10x2 

6x5 

11x2 

9x11 

3x  10 

12  x  11 

7x4 

3x3 

12x3 

9x9 

6x9 

4x  10 

7x11 

8x2 

3x2 

11x4 

8x4 

3x4 

8x11 

8x9 

5x  12 

11x6 

2x8 

2x5 

10x5 

12x7 

5x5 

7x8 

6x7 

6x8 

10x6 

6.  12  x  6 

9.  4x6 

12.  11  x  10 

9x7 

2x7 

8x8 

10  x  12 

10  x  10 

7x  12 

2x  12 

4x5 

2x3 

2x2 

9x2 

3x8 

12x8 

4x11 

11  X  11 

9x6 

6x11 

5x3 

8X  10 

11  X  9 

4x4 

7x6 

9x3 

8x7 

7x  10 

12  x  10 

7x9 

12X5 

8x6 

5x9 

10x8 

9x7 

5x7 

2x4 

6x4 

7x8 

6x  12 

11  X  7 

3x5 

6x7 

38  MULTIPLICATION    AND    ADDITION 

Drill  for  Rapidity 


1.   Add  2  to 

2.   Add  3  to 

3.   Add  4  to 

4.   Add  5  to 

3x4 

3x9 

9x  12 

7x4 

5x11 

9x2 

12x6 

5x8 

4x5 

12x7 

9x7 

9x6 

6x9 

8x11 

8x  12 

8x7 

7x  12 

3x  12 

12  x  11 

9x8 

12x5 

6x4 

8x5 

7x6 

11  X  11 

4x9 

8x9 

4x  12 

12  x  12 

3x5 

12  x  10 

8x6 

6x3 

12x3 

10  x  11 

7x9 

6.   Add  6  to 

6.   Add  7  to 

7.   Add  8  to 

8.   Add  9  to 

3x8  6x12  4x4  12  x  2 

7x3  11x12  5x12  8x2 

5x7  5x3  11x10  6x6 


9x4 

8x4 

12x8 

4x8 

8x3 

5x5 

9x9 

6x7 

9x5 

3x6 

6x5 

3x11 

7x  J 

4x7 

7x2 

5x9 

4x6 

6X8 

5x4 

7x8 

8x8 

12x4 

12x9 

5x6 

9.    16         26         36         46         56         66         76         86         96 


_8 

_8 

8 

_8 

8 

8 

_8 

8 

8 

10.    17 

27 

37 

47 

57 

67 

77 

87 

97 

8 

8 

_8 

8 

8 

8 

8 

8 

8 

11.    18 

28 

38 

48 

58 

68 

78 

88 

98 

8 

_8 

_8 

8 

8 

8 

_8 

_8 

_8 

12.    19 

29 

39 

49 

59 

69 

79 

89 

99 

8 

_8 

_8 

8 

_8 

8 

8 

8 

_8 

MULTIPLICATION  AND    SUBTRACTION  39 

Drill  for  Rapidity 

1.                                 2.  3.  4. 

Take  2  from          Take  3  from  Take  4  from  Take  5  from 

12  x  3         6x3  8x9  9x8 

3x5        12  X  12  12  x  10  7x4 

4x9         3x4  10x11  9x6 

6x4         4x5  8x12  8x7 

3x12        6x9  12x11  7x6 

8x11                    7  x  12  9x7  4  x  12 

12  x  7                    12  x  5  12  x  6  8x6 

9x2                    11x11  9x12  7x9 


5. 

6. 

7. 

8. 

Take  6  from 

Take  7  from 

Take  8  from 

Take  9  from 

7x5 

12  x 

9 

9x  11 

5x6 

8x8 

12  x 

4 

5x4 

7x8 

4x  12 

6x 

8 

7x2 

5x9 

7x7 

4x 

7 

6x5 

6x7 

9x5 

3x 

6 

9x9 

4x8 

8X3 

8x4 

12x8 

6x6 

9x4 

5x 

3 

11  X  10 

8x2 

7x3 

11  X 

12 

► 

5x  12 

7x  11 

3x8 

26 

6x 

12 

> 

4x4 

76 

12x2 

9.    16 

36 

46 

56 

66 

86         96 

9 

9 

9 

9 

9 

9 

9 

_9         _9 

10.    17 

27 

37 

47 

57 

67 

77 

87         97 

9 

9 

9 

9 

9 

9 

9 

2     J. 

11.    18 

28 

38 

48 

58 

68 

78 

88         98 

_9 

9 

9 

9 

9 

9 

J9 

_9           9 

12.    19 

29 

39 

49 

59 

69 

79 

89         99 

9 

9 

9 

9 

9 

9 

9 

_9        _9 

40 

WHOLE  : 

NUMBERS      DIVISION 

1.    18  divided  by  2 

2.      4 

-f-  2          3. 

16 

H-  2 

4.     6  +  2 

21  divided  by  3 

27 

+  3 

15 

+  3 

9^3 

24  divided  by  4 

8 

^4 

32 

^4 

28  +  4 

40  divided  by  5 

25 

+  5 

10 

+  5 

20-5 

36  divided  by  6 

24 

+  6 

18 

+  6 

42-6 

21  divided  by  7 

63 

■*  7 

49 

+  7 

28  *  7 

40  divided  by  8 

48 

+  8 

72 

+  8 

56-8 

18  divided  by  9 

45 

+  9 

72 

^9 

54-9 

33  divided  by  11 

77 

4-  11 

44 

+  11 

99  -  11 

96  divided  by  12 

24 

+  12 

84 

+  12 

60-  12 

5.    2)46 

6.    3)84      7. 

4)84 

8.    5)95 

9 

.  6)120 

10.    7)91 

2)54 

3)96 

4)96 

5)100 

6)150 

7)210 

2)88 

3)69 

4)44 

5)80 

6)96 

7)147 

2)62 

3)52 

4)76 

5)75 

6)90 

7)98 

2)50 

3)78 

4)56 

5)125 

6)132 

7)154 

2)72 

3)57 

4)68 

5)90 

6)144 

7)105 

2)96 

3)81 

4)88 

5)105 

6)108 

7)161 

2)78 

3)90 

4)72 

5)150 

6)84 

7)224 

11.    2)264 

12.    7)252 

13. 

3)654       : 

L4. 

5)650 

15.    2)270 

3)357 

4)252 

4)340 

6)372 

3)270 

6)624 

6)192 

7)714 

4)372 

4)900 

4)516 

2)508 

6)240 

3)810 

6)450 

5)720 

5)375 

2)500 

7)350 

7)364 

WHOLE  NUMBERS      DIVISION 


41 


1.  10-5-2 

2.   14-5-2 

3. 

12 

-  2 

4.  8-5-2 

6^-3 

24-5-3 

12 

-5-  3 

18-5-3 

36^-4 

12-5-4 

20 

-4 

16-4 

15-5-5 

30-5-5 

35 

+  5 

45-5 

30^-6 

48+  6 

54 

-5-  6 

12-6 

14-7 

35  +  7 

42 

+  7 

56-5-  7 

24  +  8 

64-8 

32 

+  8 

16-s-  8 

63-9 

27-5-9 

81 

-5-9 

36-5-9 

55  +  11 

88-5-  11 

22 

-  11 

66  h-  11 

48-s-  12 

108  -5-  U 

► 

72 

-  12 

36  +  12 

5.  8)640   6. 

9)198   7. 

10)640 

8. 

11)341 

9.  12)252 

8)128 

9)270 

10)210 

11)572 

12)600 

8)256 

9)927 

10)700 

11)132 

12)132 

8)328 

9)153 

10)350 

11)187 

12)384 

8)816 

9)468 

10)200 

11)209 

12)504 

8)560 

9)945 

10)470 

11)165 

12)708 

8)808 

9)207 

10)110 

11)440 

12)288 

8)488 

9)846 

10)600 

11)693 

12)192 

10.  7)3500 

11.  8)6000 

12. 

11)2530 

13.  8)8056 

8)6480 

11)4510 

8)1616 

12)1440 

9)8109 

7)1428 

12)4800 

11)3410 

11)5533 

12)6036 

6)3606 

9)2070 

12)6012 

9)4680 

9)9045 

6)6048 

42 


WHOLE   NUMBERS      DIVISION 


1. 

2. 

3. 

4. 

5. 

6. 

9)36             4)60 

12)36 

8)64 

12)132 

8)72 

12)72            3)45 

4)48 

12)96 

7)28 

4)28 

7)35            5)40 

11)11C 

I 

7)21 

8)32 

7)84 

11)66           11)132 

6)24 

3)15 

12)120 

9)45 

12)60           12)48 

8)24 

5)60 

3)18 

12)108 

9)27            8)56 

12)24 

12)84 

5)30 

11)44 

6)42            7)63 

5)45 

6)36 

7)42 

4)24 

4)32             9)72 

3)27 

4)20 

6H8 

10)120 

7.    12  4-  ?  -  4 

8. 

28- 

-  ?  =  4 

9.     72  - 

-  ?  =  6 

27- 

-  ?  =  9 

42- 

-  ?  =  7 

56- 

-  ?  =  8 

44- 

-  ?  =  4 

L08- 

-  ?  =  12 

132- 

-  ?=  11 

36- 

-  ?  =  6 

84- 

-  ?  =  7 

110- 

-  ?=  10 

81  - 

-  ?  =  9 

54- 

-  ?  =  6 

42- 

-  ?  =  7 

72- 

-  ?=  12 

35- 

-  ?  =  7 

54- 

-  ?  =  6 

63- 

-  ?  =  9 

42- 

-  ?  =  6 

64- 

-  ?  =  8 

56- 

r  ?«7 

63- 

-  ?  =  7 

84- 

-  ?  =  12 

10.    Count  by  25 

's  to  600. 

11. 

Count  by  75jj 

3  to  900. 

12.    15)600     13. 

50)600     1 

L4.   1 

5)450     15.   25)200     16 

75)150 

20)400 

60)720 

1 

6)320 

25)300 

75)300 

25)500 

70)770 

2 

1)420 

25)150 

75)225 

30)330 

80)960 

2 

52)880 

25)450 

75)600 

40): 

L60 

90)270 

2 

4)720 

25)600 

75)750 

DIVISION      DRILL  FOR  RAPIDITY  43 


Divide  by  2 : 

1.  20 

42 

36 

44 

26 

60 

32 

28 

2.  18 

50 

22 

40 

58 

46 

38 

62 

3.  34 

52 

24 

30 

48 

64 

56 

66 

4.  54 

70 

90 

84 

78 

80 

92 

68 

5.  86 

94 

82 

74 

96 

72 

88 

76 

Divide  by  3 : 

1.   12 

21 

42 

15 

36 

24 

30 

18 

2.  27 

45 

33 

51 

39 

48 

57 

69 

3.  54 

81 

60 

84 

75 

66 

72 

93 

4.  78 

90 

87 

99 

63 

96 

120 

102 

5.  Ill 

129 

105 

126 

117 

108 

123 

114 

Divide  by  4 : 

1.  20 

44 

72 

28 

36 

16 

24 

12 

2.  40 

56 

68 

52 

76 

60 

48 

64 

3.  80 

96 

84 

92 

88 

32 

120 

160 

4.  104 

144 

116 

136 

168 

124 

108 

132 

5.  140 

156 

112 

152 

148 

164 

100 

128 

Divide  by  5 

1.  60 

15 

30 

70 

55 

35 

75 

10 

2.  50 

95 

20 

90 

65 

40 

85 

25 

3.  80 

45 

100 

120 

160 

105 

135 

150 

4.  110 

140 

180 

115 

165 

190 

125 

155 

5.  130 

170 

200 

175 

205 

195 

145 

185 

Divide  by  10 : 

1.  120 

210 

150 

110 

240 

130 

170 

200 

2.  190 

300 

140 

160 

220 

180 

250 

230 

44  DIVISION      DRILL    FOR    RAPIDITY 


Divide  by  6 

1.  12 

66 

24 

84 

42 

96 

54 

60 

2.   18 

72 

30 

90 

36 

48 

78 

102 

3.  114 

174 

132 

108 

150 

138 

186 

120 

4.  156 

126 

144 

192 

162 

198 

168 

180 

5.  240 

204 

234 

246 

216 

228 

210 

222 

Divide  by  7 

* 

1.  21 

70 

91 

14 

84 

56 

28 

49 

2.  63 

77 

35 

98 

42 

105 

140 

126 

3.  147 

154 

133 

168 

182 

161 

119 

189 

4.  112 

175 

196 

210 

280 

203 

245 

266 

5.  238 

259 

224 

273 

252 

231 

217 

287 

Divide  by  8 : 

1.  88 

40 

16 

56 

32 

64 

24 

72 

2.  96 

48 

80 

104 

160 

144 

112 

136 

3.  120 

176 

128 

152 

184 

168 

192 

240 

4.  200 

280 

232 

208 

256 

216 

264 

224 

5.  248 

272 

296 

288 

320 

304 

328 

312 

Divide  by  9 : 

1.  90 

45 

72 

99 

36 

81 

54 

18 

2.  27 

63 

108 

135 

180 

117 

153 

198 

3.  144 

171 

126 

189 

162 

207 

243 

270 

4.  216 

252 

288 

234 

225 

261 

279 

297 

6.  306 

333 

360 

342 

315 

369 

351 

324 

Divide  by  11 

1.  110 

209 

121 

220 

165 

231 

198 

132 

2.  264 

187 

143 

176 

154 

253 

275 

242 

DIVISION  45 
How  many  times,  and  how  many  over? 

1.  6)50  4)30  8)25          10)36            7)40  8)60 

2.  4)21  3)18  8)42            5)19          12)63  8)75 

3.  5)28  10)42  9)46            3)17          12)80  10)37 

4.  4)45  3)22  6)67            7)56            8)70  5)18 
6.    12)33  11)56  9)29            4)32            6)62  8)49 

6.  9)88  11)76  5)54_           7)55            4)37  6)52 

7.  12)100  15)35                6)130              5)182  3)205 

8.  3)100  25)54                8)165              4)330  6)320 

9.  8)100  30)95              12)200             9)640  7)135 

10.  6)100  20)83                9)125              6)254  4)163 

11.  7)100  12)150              7)368  12)302  8)334 

12.  9)100  40)125            11)452              8)250  5)481 

13.  13)28  24)55              35)80  14)56  21)75 

14.  50)112  16)48              75)160  44)90  37)60 

15.  15)75  28)60              33)100  61)125  70)300 

16.  36)80  55)165            80)250  45)53  22)100 

17.  17)51  23)80             42)100  93)200  56)75 

18.  30)160  18)90              36)45  19)62  66)80 


46  WHOLE  NUMBERS      DIVISION 


How  many 
1.     3)16 

times,  and  how  many 
2)21            5)18 

over? 

4)25 

3)28 

6)21 

2. 

4)19 

3)25 

2)15 

6)39 

5)23 

3)14 

3. 

6)50 

4)30 

8)25 

10)36 

7)40 

10)57 

4. 

4)21 

3)32 

8)42 

5)19 

12)63 

8)60 

5. 

5)28 

10)42 

9)76 

3)T7  . 

12)80 

8V75 

6. 

4)45 

3)22 

6)67 

7)56 

8)70 

5)16 

7. 

12)33 

11)56 

9)29 

4)35 

6)62 

8)49 

8. 

9)88 

11)76 

5)54 

7)55 

4)37 

6)52 

9. 

5)48 

2)T7 

3)35 

4)18 

9)40 

5)34 

10. 

8)36 

6)40 

5)58 

3)10 

7)44 

11)40 

11. 

5)42 

3)29 

4)23 

6)25 

8)54 

7)33 

12. 

3)23 

3)11 

3)19 

3)23 

3)31 

3)38 

13. 

4)13 

4)42 

4)34 

4)26 

4)38 

4)49 

14. 

5)12 

5)56 

5)41 

5)36 

5)27 

5)52 

15. 

6)20 

6)16 

6)33 

6)45 

6)27 

6)55 

16. 

7)17 

7)50 

7)25 

7)38 

7)62 

7)75 

17. 

8)28 

8)83 

8)26 

8)44 

8)38 

8)52 

18. 

9)35 

9)70 

9)50 

9)67 

9)31 

9)22 

19. 

11)80 

11)30 

11)60 

11)20 

11)50 

11)90 

20. 

12)50 

12)65 

12)44 

12)27 

12)18 

12)99 

DIVISION  47 

Division  is  expressed  in  two  ways.  The  division  of  2  by  5  may 
be  expressed  "2  +  5"  or  "f." 

Read  the  following  expressions  as  fractions.  Tell  whether  each 
fraction  is  proper  or  improper.  Change  improper  fractions  to 
whole  numbers,  and  proper  fractions  to  lowest  terms. 

1.    12  -  4  2.     6  +  3  3.     3  -  6  4.     6  -  18 

9-3  20-10  14  -  7  4-20 

8-16  16-4  4-12  5-20 

5-10  8-2  8-4  10-2 

4-2  5-15  2-8  4-16 

10-5  3-12  7-14  3-9 

16-8  15-3  3-3  2-4 

2-14  12-2  18-9  12-16 


Read.     Change  to  fractional  form.     Reduce. 

5.   8  -  12  6.     7  -  49          7.    16  -  24            8.   45  -  60 

4-16  8-56  24-36  15-21 

6  +  48  15-25  30  -  40  14  -  77 

7-21  6-28  9-15  54  -  60 

9-63  4-18  32-40  16-72 

8-40  12-18  27-36  5-30 

3-18  9-9  40-64  12-20 

4-32  21-35  36  -  42  40  -  50 


Read  as  fractions.     Reduce  where  possible  to  do  so. 

9.     2  -  3            10.     8  -  20        11.    100  -  8          12.  5  -  100 

80-9                    2-50               100-3  4-100 

25  -  100              25-5                 100-6  10  -  100 

4-5                    6-7                 100-7  25-100 

3  +  11                  5+10              100  -  12  50  -  100 


48  ALL  THE   FACTS  OF  THE   DIVISION  TABLES 


Drill  for  Rapidity. 

1.  18-9 

4.  24-2 

7.  36  4-  12 

10.   8v2 

50-  10 

20-4 

90-9 

27  ^9 

36-4 

36-6 

55  -  11 

33-3 

55-5 

88-8 

60-  10 

90-  10 

30-3 

20-  10 

10-2 

40-8 

12-2 

132  4-  12 

24-3 

18-6 

72-8 

21-3 

70-7 

35^-5 

48-  12 

40-5 

32-8 

40-4 

33-  11 

49-7 

12-6 

28-7 

30-6 

36-9 

48-4 

110  4-  11 

2.  21-7 

5.  22  +  11 

8.  45  4-  5 

11.  108  -  12 

96-  12 

14-2 

108  h-  9 

12-3 

18-3 

99  +  11 

20-2 

30-5 

22-2 

9-3 

30-  10 

132  4-  11 

28-4 

40-  10 

36-3 

81-9 

54-9 

44^-4 

77  4-  11 

.   16-2 

6-2 

72-9 

32^4 

12 -h  4 

88  -  11 

10-5 

60  4-  12 

.66-6 

16-8 

56^-8 

50-5 

84-7 

25-5 

72-6 

42-7 

48-8 

3.  60-6 

6.   14-7 

9.  24-6 

12.  110  -  10 

63-7 

24-  12 

64-8 

120  4-  12 

100  -  10 

4-2 

84  -  12 

20-5 

6-3 

44-  11 

18-2 

24^-8 

96-8 

15^3 

121  -  11 

54 -h  6 

66  -  11 

42 -h  6 

80-  10 

99  +  9 

16^-4' 

120  -  10 

27-3 

56-7 

70-  10 

45-9 

63-9 

60-5 

48-6 

8-4 

80-8 

63  +  7 

35-7 

144  -  12 

24^-4 

56  +  8 

72^-  12 

77 -'7 

15^5 

42  +  7 

MULTIPLICATION  AND  DIVISION  49 


1.   Divide  by  4  : 

2.   Divide  by  6  : 

3.   Divide  by 

6x6 

4x9 

12x2 

8X6 

9x8 

2X20 

3x8 

2x  12 

6x  12 

6x2 

12x5 

2x4 

8x2 

3x4 

16X2 

2x  10 

2x30 

4x  12 

8X5 

9x2 

4x4 

ride: 

4.   4  X    5  by  2  X  2. 

5. 

8  X  12  by  3  X  4. 

6  X    6  by  3  X  2. 

6  X  10  by  2  x  5. 

8  X    6  by  4  X  3. 

9x    2  by  3  X  2. 

2  X  12  by  2  X  2. 

7  X    4  by  2  X  2. 

6.    10  X  4  by  5  x  2. 

7. 

10  x  10  by  5  X  5. 

6  X  7  by  2  x  3. 

8  X    9  by  3  x  4. 

8  X  3  by  2  x  2. 

6  X  11  by  2  X  3. 

5  X  8  by  2  x  4. 

12  x    6  by  3  X  3. 

8.  3x4x5  divided  by  2  X  2  =  ? 

9.  3x3x8  divided  by  2  X  3  X  2  =  ? 

10.  4  x  10  X  3  divided  by  2x2x5=? 

11.  8x5x2  divided  by  2  X  5  =  ? 

12.  9x5x2  divided  by  3  X  3  =  ? 

13.  3x7x4  divided  by  3x2x2=? 

14.  5x7x2  divided  by  2  X  5  =  ? 

15.  6x5x4  divided  by  2x2x2=? 

16.  10  X  10  X  2  divided  by  5  X  5  =  ? 

17.  2  X  8  X  10  divided  by  5  X  2  =  ? 


50        PRACTICE  IN  INTERPRETING  SIGNS  QUICKLY 


1. 

5-3  = 

7  +  2  = 
9-1-3  = 
8-5  = 
2x4  = 
6  +  7  = 

18-2  = 
6x3  = 
9-4  = 

8+11  = 


132  +  12  - 

150  -  25  = 
12  x  20  = 

135  +  15  = 
75  -  25  = 
50  +  15  = 
64x2  = 
175  -  5  = 
80  x  12  = 

100  -  54  = 


2. 

3x3  = 
16-7  = 

8  +  5  = 
20-4  = 
14-2  = 
3+  11  = 
15-7  = 
7  +  8  = 
4x5  = 
12  +  8  = 


3. 

15-5  = 

4x4  = 

5+  11  = 

19-7  = 

12-3  = 

11  +4  = 

8-2  = 

16-9  = 

3x5  = 

7  +  11  = 


10. 

60x6  = 

140  -  32  = 

70  +  35  = 

250  -  50  = 

100  -  22  = 

300  -  15  = 

7x21  = 

33  +  18  = 

95  -  42  = 

144  -  12  = 


11. 

55  X  2  =  ? 
108  -  36  =  ? 

43  +  62  =  ? 

88  -  27  =  ? 

39  +  26  =  ? 

165  -  15  =  ? 

16  x  6  =  ? 

80  -  48  =  ( 

48  -  16  =  ? 

50  X  12  =  ? 


4. 
12-2  = 
4+15  = 

8-3  = 

7  +  9  = 
15-3  = 

2x8  = 

12-9  = 

5x4  = 

20  -  11  = 

8  +  8  = 


12. 

13x3  = 

225  -  25  = 

105  -  40  = 

18  +  54  = 

72  -  36  = 

100  -  14  = 

96  -  16  = 

50  +  75  = 

5x25  = 

75  -  15  - 


5. 

6. 

7. 

8. 

24  +  8  =  ? 

12  x  5  =  ? 

88  +  11  = 

? 

48  +  6  =  ? 

49  -  7  =  ? 

96-8=  ? 

64-8  = 

? 

8x7=? 

63  -  7  =  ? 

56  +  7  =  ? 

96  -  12  = 

? 

36  +  12  =  ? 

8x9=  ? 

7x8=  ? 

42-  7  = 

? 

60  -  12  =  ? 

14  +  14  =  ? 

45  -  9  =  ? 

32  +  8  = 

? 

35  -  7  =  ? 

56  -  7  =  ? 

8  X  12  =  ? 

27-  3  = 

? 

18  +  9  =  ? 

42  -  6  =  ? 

40  +  8  =  ? 

9x6  = 

? 

84  -  7  =  ? 

12  x  7  =  ? 

36  -  4  =  ? 

54-9  = 

? 

81  -  9  =  ? 

36  +  9  =  ? 

72  -  6  =  ? 

28-  7  = 

? 

40  -  4  =  ? 

84  -  12  =  ? 

40  -  5  =  ? 

42-  6  = 

? 

35  +  7  =  ? 

PRACTICE   IN  INTERPRETING  SIGNS  QUICKLY         51 

Tell  whether  your  answer  is  product,  quotient,  sum,  or  re- 
mainder. 

1.       3x4  2.       3x7  3.     2  X  11  4.      16  +  4 

7  +  8  35-5  36-4  25-7 
18-3  5  +  7  4  +  8  17  +  7 

9-5  11-5  21-7  9x3 

14  +  5  32-8  18-9  49-7 

3x9  9  +  8  12  +  6  11  +  6 

24-3  20-9  25-5  28-7 

5x4  6x5  3x3  7x5 

11-2  5  +  12  11-8  36-6 

8  +  3  24-12  6  +  7  17-9 


5  +  8 

6.     2  X  15 

7.     35-7 

8.       9x9 

8x7 

45-5 

18  +  7 

14  +  5 

42-7 

18  +  5 

56-7 

25-9 

17-8 

15-7 

6x  12 

60-5 

6x9 

7x9 

7  +  9 

12x5 

63-7 

108-9 

48-6 

44-  11 

.4+11     . 

8  +  7 

22-8 

17-9 

7x6 

23-7 

54-9 

13  +  12 

13-5 

9x6 

6x  11 

8x8 

40-4 

60-2 

34-  6 

45-9 

9.  125  -  5   10.  75  -  15    11.  102  -  12    12.  34  +  28 

14  x  4  300-25  20  X  5  50  -  18 

18  +18  80  -  16  150  -  3  75-62 

600  -  12  18  X  5    .  250-2  120  -  40 

20  x  8  17  +  17  12|  x  8  40-15 

75  +  50  33-8  6ix4  16x4 

225  -  75  180  -  6  100-3  15  X  5 

45-3  11  X  12  100  -  6  30-16 

14  x  3  144  -  2  33|  X  2  360  -  12 

96  -  16  33  +  17  12|  x  3  100  -  62 


52        PRACTICE    IN    INTERPRETING    SIGNS    QUICKLY 

How  many  of  these  questions  can  you  answer  in  one  minute  ? 
Answer  in  complete  statements. 

1.  7       12         6       15         28          8       48         18       16  25 
-^-f^xJ+S      -9      X7    +6       -_5     +_7  -_12 

2.  12       27       11       34         15         14       12         40       18  9 

X  7     -3     +_8     ^       -7      +8     X^3     -  11     +  7  x4 

3.  17       25       15       40         50    '     50         8           8         8  14 

+  5     -6x2     -5     +25     -25     -8       X8+8  -9 


5x2-3  = 

?      1 

5.       9x8h-6  = 

? 

6.   30  +  15  +  2  = 

? 

6+2x7= 

? 

12  -  7  X  5  = 

? 

6  +  5-  11  = 

? 

7  -  4  +  12  = 

? 

18  -  9  +  1  = 

? 

25  -  20  x  7  = 

? 

16  +  8  X  10  = 

? 

3x7+5= 

? 

14  -  7  x  8  = 

? 

7x7-7  = 

? 

4+4x4= 

? 

6.6x6= 

? 

22  -  11  x  6  = 

? 

13  +  3  +  8  = 

? 

8  X  9  +  12  = 

? 

8x5-2= 

? 

10  -  10  +  3  = 

? 

.  3  +  11  -s-  7  = 

? 

3+3x6= 

? 

9x1-8= 

? 

20  -  5  -  4  = 

? 

Tell,  as  you  answer  the  questions  below,  whether  your  answer 

is  called  sum,  product,  quotient,  or  remainder. 

7.    132  -  11  =  ?  8.    175  -r  25  =  ?  9.        14  X  3  =  ? 

12  x  20  =  ?  8  X  20  =  ?  80  +  20  =  ? 

54  +  16  =  ?  100  -  48  =  ?  25  x  8  =  ? 

39  -r-  13  =  ?  96  -^  16  =  ?  45  -  8  =  ? 

16  X  5  =  ?  19  +  19  =  ?  100  -  5  =  ? 

17  +  17  =  ?  96  -^  12  =  ?  16  x  3  =  ? 

60  +  15  =  ?  20  x  20  =  ?  13  +  25  =  ? 

25  X  5  =  ?  36  -  2  =  ?  108  *  12  =  ? 


RELATION    OF  NUMBERS 


53 


6  is  what  part 

4  is  what  part 

5  is  what  part 
3  is  what  part 

1  is  what  part 

7  is  what  part 

2  is  what  part 
10  is  what  part 

8  is  what  part 

9  is  what  part 


of  12? 
of  16? 
of  15? 
of  9? 
of  5? 
of  14? 
of  10? 
of  60? 
of  24? 
of  36? 


2. 


What  part  of  30  is  15? 
What  part  of  55  is  11? 
What  part  of  100  is  20? 
What  part  of  75  is  25? 
What  part  of  144  is  12? 
What  part  of  150  is  50? 
What  part  of  60  is  15? 
What  part  of  80  is  40? 


5  is  what  part 

8  is  what  part 

2  is  what  part 

9  is  what  part 
10  is  what  part 

6  is  what  part 

3  is  what  part 

7  is  what  part 
1  is  what  part 

4  is  what  part 


of  30? 
of  40? 
of  6? 
of  18? 
of  40? 
of  48? 
of  21? 
of  63? 
of  12? 
of  20? 


4.   What  part  of  150  is  75? 
What  part  of  300  is  75? 
What  part  of  45  is  15? 
What  part  of  88  is  11? 
What  part  of  44  is  22? 
What  part  of  200  is  25? 
What  part  of  48  is  16? 
What  part  of  96  is  12? 


Nine  is  what  part  of  twelve  ? 
Eight  is  what  part  of  twelve  ? 
Six  is  what  part  of  nine? 
Four  is  what  part  of  six? 
Eight  is  what  part  of  ten  ? 
Fifteen  is  what  part  of  twenty  ? 
Twelve  is  what  part  of  sixteen  ? 
Fourteen  is  what  part  of  twenty- 
one? 


Twenty  is  what  part  of  thirty  ? 
Twelve  is  what  part  of  eighteen  ? 
Ten  is  what  part  of  twenty-five  ? 
Sixteen  is  what  part  of  twenty  ? 
Nine   is   what  part  of  twenty- 
one? 
Twelve  is  what  part  of  fifteen  ? 
Thirty  is  what  part  of  fifty  ? 
Ten  is  what  part  of  twelve  ? 


For  Ratio,  and  its  use  in  solving  simple  problems,  see  Appendix. 


54  CANCELLATION 

State  results  only : 

1.  2.                         3.  4. 

.12x5  8x  10  3x  14  9x4 

6  5                        7  "  3 
24x9  40x3  2x25  49  x  10 

8  10                     5  7 

5x  16  20x2  8x  36  33x5 

8  4                        9  11 

21  x  2  10x48  6^x  5  81  xU 

7  12                     9  9 
28  x  12  6  x  35  10  x  42  50  x  5 


6. 

15x8 

5 
60  x  11 

30 
30x7 

5 
9x7 

3 
77x2 

10  11 


6.                                  7.                               8.  9. 

2x3x3  3x4x2  3x4x12  5x2x3 

9                               8                             16  25 

3  x  1  X  100  7x8x5  4x2x11        .      5  x  12  x  1 

10                           35                            44  6 

5  x  3  x  20  3  x  64  x  1  3x4x2  5  x  36  x  2 

20                              8                           12  18 

2  x  3  x  35  9  x  55  x  2  6  x  7  x  12  7x6x6 

7                              11                           24  42 

14  x  3  x  5  5  x  18  X  1  40  x  10  X  3  15  x  8  X  1 

2                              9     '                       20  "30 


10.  11.  12.                          13.  14. 

48  x  12  60x7  65x5  75x8  200x3 

16  5  13         15  25 

96  x  7  140x8  132x6  7  x  54  35  x  5 

16  20  11         18  7 

120  x  5  200x9  200  x  11  132x4  34  x  5 

30  50  88         44  17 

25  x  3  80x7  72  x  3  60  x  12  100  x  1 

25  16  24          24  5 


CANCELLATION  55 


State  results: 

1. 

2. 

3. 

4. 

5. 

10  x  7 

9x4 

12x7 

5x6 

3x15 

5 

18 

36 

30 

5 

6x8 

7x2 

44x3 

3x  17 

4x5 

32 

14 

11 

15 

25 

3x8 

15  x  7 

10  x  13 

5x2 

35x4 

27 

28 

26 

8 

7 

10x7 

8x7 

7x5 

5x  18 

16  x  7 

21 

40 

25 

10 

4 

9x11 

64  x  5 

21  x  6 

12x5 

2x  16 

99 

8 

3 

30 

4 

6. 

7. 

8. 

9. 

2x3x3 

5  X  4  X 

2 

3x  2 

X8 

5 

X  2x  7 

4 

8 

16 

35 

3  X  3  x  10 

7x8x4 

6x2 

X  11 

5  X  12  x  1 

100 

40 

33 

3 

60  x  5  X  2 

5x  6x 

7 

9x2 

x  10 

5 

X4x  10 

30 

12 

5 

20 

4x8x1 

5  X  5  X 

3 

3x4 

X2 

2 

X3x2 

64 

25 

24 

33 

6x3x2 

2x3x 

18 

9X  11 

X2 

2 

X  1  X  7 

60 

6 

55 

6 

10. 

11. 

12. 

13. 

14. 

5x7 

8x7 

4x  18 

9x9 

6x7 

4x  15 

21x2 

9x2 

35x2 

5x2 

7x2 

15x4 

8x9 

50  x  2 

2X  11 

20  x  3 

2x3 

3x24 

5x25 

44  X  12 

27  x  50 

16x25 

4x7 

13  x  2 

11X4 

9x  100 

5x2 

7x  12 

8X5 

3x33 

80x5 

56x7 

5x45 

12  X  12 

7x90 

1x20  7x8  10  x  9  3x3  45  x  2 


56  CANCELLATION 


Give  results 
1. 
3 

2. 

8 

3. 

11 
7x  22 

20 
3x  15 

32 
11  X  8 

11 
44  x  5 

21 
3x4 

4. 

15 
6x5 

8 
5x2 

75 
4x25 

25 

5x8 

5 

3 
3 
5 
6 

5. 
36 

7x6 
10 

32  x  5 
4 

7x  12 

7 

5x5 
30 

17x2 
3 

4x35 
9 

12x5 

18 

27x4 
2 

6x2 
49 

12x6 
10 

7x  10 

35 
14x5 

7x3 
6 

5x  14 

8X35 

10  x  18 

6. 
21 

7. 
12 

7 
4 
4 

8. 

56 

9. 
44 

5x3x7 
32 

8x4x5 
45 

X  2x  1 
6 

X  11X5 
15 

5x8x3 
11 

9x2x5 

8 

x  l: 

16 

X  12 

X45x  2 
50 

2  x  33  X  5 

20 

2x8x5 
60 

x  3: 

72 

X5 

X2x  7 
36 

7x5x3 

8 

15  X  1  X  4 

7 

9 

x2: 
18 

<2 

X  5x  2 
25 

3  X  24  X  5 

35  x  3  x  3 

l              2 

x  7 : 

X9 

3 

X  100  X  2 

10. 
20x7 
14x60 
6x32 
8x3 
16x3 
5x24 
2x  18 

11. 
18  X  15 
45x3 
5x  12 
48X3 
4x7 
9x8 
27x3 

12. 
7x  23 
10x21 
6x2 
4x9 
5x  14 
35  x  2 
60  x  12 

13. 

50x4 
3x  25 
5x  11 
88x8 
56  X  3 
6x8 
2x21 

14. 
16x5 

5x8 
12  x  20 

5x8 
63  X  5 
9x  10 
48  X  2 

24  X  2  9x2  4x15  5x7  20  x  6 


CANCELLATION  57 


Give  results  : 

1.   7  x  12 

2.       3 

3.   3  X  5 

4.   9x6x2 

6 

7x6 

6x3 

12 

8x5 

12 

10x8 

8x3x5 

20 

60x3 

4x5 

4 

7x30 

45 

3x7 

7x2x11 

21 

2x9 

6x21 

14 

9x8 

8 

8x2 
3x40 

5  x  9  x  12 

3 

16x7 

36 

10  x  11 

33 

4x9 

7  x  25  x  2 

44 

7x11 

27  x  2 

50 

3x25 

10     ' 

5x  12 

40  x  2  X  5 

5 

5x8 

6x  10 

20 

6.   5x4 

6.        4 

7.   9  x  11 

8.    10  x  11  X  8 

36 

12x7 

8X33 

90 

6x7 

20 

15x4 

2  x  3  x  28 

42 

15x4 

8X3 

7 

2x9 

7 

10x25 
5x2 

6  x  15  x  2 

27 

6x35 

75 

50x4 

48 
6x5 

36x3 
12x4 

15 

40 

3x4x2 

28x5 

18 

18x4 

48 

7 

9x  10 

2x27 

8x5x5 

9.    4X  11 

10.      63 

11.    7x8 

12.           8 

20 

4x7 

24x3 

3x5x24 

10  X  18 

30 
8X  15 

12  x  11 
7x60 

22 

9 

55  X  4  X  7 

12x7 

22x6 
11 

25x6 
3x  50 

6 

60 

9x4x5 

8X7 

26x4 
13 

8x9 
5x  16 

84 

49 

7  x  10  x  2 

6x9 

30 
6x7 

7x  15 
45x49 

56 

45 

9x5x5 

58 


Name  two  factors  that  make 


1. 


4 

6 

8 

9 

10 

12 

14 

15 


2. 


16 
18 
20 
21 
22 
24 
25 
27 


FACTORS 

lake 

28    4.  44 

5.  60 

30      45 

63 

32      48 

64 

33      49 

66 

35      50 

70 

36      54 

72 

40      55 

75 

42      56 

77 

Name  two  groups  of  factors  making 

1.   30  2.    36  3.   40  4.    20 

18  16  48 


42 
60 
12 


72 
24 


80 

28 


Name  the  two  equal  factors  of 

1.     9  2.    25  3.     4  4. 

64  81  49 


90 
32 


16 
100 


Separate  each  of  these  numbers  into  3  factors : 

1.   27  2.    16  3.    66  4.   50  5.  56 

12  24  20  28  32 

63  60  48  72  18 

40  45  30  80  70 


Name  two  factors  common  to 


6. 


80 

81 
84 
88 
90 
96 
99 
100 


50 

6. 

150 

100 
200 

160 
180 

120 

240 

36 

6. 

144 

121 

400 

1. 


12  and  18 
24  and  36 
15  and  30 
14  and  42 
18  and  36 


50  and  30 
64  and  80 

21  and  63 

22  and  132 
35  and  70 


3. 


6.  36 

90 

44 

75 

28  and  56 

54  and  66 

40  and  64 

45  and  30 

75  and  90 

FACTORS      PRIME   AND   COMPOSITE   NUMBERS         59 

1,  2,  3,       5,       7, 11,  13, 17,  19, 

4,       6,       8,  9,  10,   ~     12,         14,  15,  16,         18,         20. 

Can  the  numbers  above  the  line  be  separated  into  factors? 
Can  the  numbers  below  the  line  be  separated  into  factors? 
What  name  is  given  to  numbers  which  cannot  be  factored? 
What  name  is  given  to  all  other  numbers? 
Learn  the  prime  numbers  from  1  to  20. 
Learn  the  composite  numbers  from  1  to  20. 


All  the  composite  numbers  under  100  can  be  divided  by  some 
number  less  than  10. 

Tell  whether  each  of  the  following  numbers  is  prime  or  com- 
posite : 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

9 

29 

65 

20 

32 

76 

96 

88 

22 

28 

35 

62 

24 

31 

69 

16 

55 

97 

61 

54 

71 

43 

83 

66 

86 

48 

19 

68 

52 

89 

11 

26 

14 

47 

92 

17 

33 

21 

77 

72 

44 

15 

36 

25 

12 

30 

46 

45 

93 

84 

27 

73 

70 

81 

49 

64 

34 

53 

40 

75 

59 

95 

57 

90 

67 

41 

37 

99 

98 

80 

13 

50 

18 

51 

38 

58 

60 

87 

39 

91 

82 

85 

10 

78 

94 

79 

74 

56 

23 

63 

Separate  the  following  numbers  into  their  prime  factors : 

1.   21      2.   60     3.   27     4.   48      5.    64      6.   99      7.   49      8.   82 


36 

55 

39 

66 

70 

25 

35 

30 

40 

32 

80 

84 

33 

34 

28 

57 

88 

90 

22 

12 

26 

95 

56 

72 

63 

75 

45 

24 

81 

20 

18 

93 

54 

44 

50 

77 

46 

96 

51 

62 

60  FACTORS  AND  MULTIPLES 

What  prime  numbers  will  exactly  divide 


1.    18? 

2.   80?        3. 

48? 

4.    56?         1 

J.   22? 

6.   25? 

84? 

45? 

90? 

21? 

35? 

44? 

50? 

30? 

63? 

33? 

40? 

15? 

20? 

64? 

36? 

42? 

72? 

39? 

66? 

32? 

54? 

70? 

49? 

75? 

24? 

81? 

60? 

27? 

28? 

96? 

Name  the  greatest  number  that  will  exactly  divide 

7. 

8. 

9. 

10. 

9  and  12 

20  and  40 

12, 

18,  and  30 

30,  60, 

and  75 

10  and  12 

15  and  30 

10, 

20,  and  45 

22,  33, 

and  77 

10  and  15 

30  and  50 

9, 

12,  and  15 

8,  12, 

and  20 

16  and  24 

14  and  28 

15, 

21,  and  30 

18,  27, 

and  63 

18  and  30 

21  and  35 

8, 

24,  and  40 

30,  36, 

and  60 

24  and  36 

32  and  56 

21, 

42,  and  56 

10,  11, 

and  12 

30  and  45 

40  and  64 

2, 

3,  and  4 

15,  18, 

and  33 

20  and  25 

12  and  36 

14, 

28,  and  7 

4,  12, 

and  20 

Name  the  least  number  that  will  exactly  contain 

11. 

12. 

13. 

14. 

4  and  6. 

7  and  8 

2, 

4,  and  6 

3,4, 

and  9 

5  and  8 

8  and  12 

3, 

2,  and  4 

12,  2, 

and  3 

2  and  11 

6  and  8 

5, 

10,  and  12 

2,  5, 

and  20 

7  and  3 

8  and  24 

2, 

4,  and  5 

4,  3, 

and  9 

8  and  4 

9  and  5 

8, 

4,  and  16 

6,  5, 

and  15 

4  and  10 

6  and  15 

3, 

5,  and  10 

12,  3, 

and  5 

6  and  9 

10  and  15 

7, 

2,  and  4 

3,  4, 

and  5 

3  and  12 

6  and  7 

3, 

6,  and  18 

6,  7, 

and  14 

COMMON  FRACTIONS     REDUCTION 


61 


Change  to  whole  or  mixed  numbers  : 


2. 


3. 


6. 


8. 


4 
2" 

9 

15 

25 
5 

40 
TO 

32 

8 

66 
1  1 

60 
T5- 

6 

12 

48 
8 

63 

36 
-3- 

18 
"9" 

60 
1  2 

84 
12 

t 

1  5 
~3~ 

18 
~2~ 

56 

7 

48 
6 

56 

"8" 

64 

"8~ 

80 

"8 

3 
3 

21 

7 

16 

if 

49 

7 

44 
1  1 

45 
5 

70 

99 
~9 

10 

20 
-5- 

35 

~5~ 

45 
~9~ 

27 
"3" 

9 
9 

72 
T2 

63 

"T~ 

14 
"7" 

24 

12 
T2- 

42 
6 

28 
"4* 

42 
7 

75 
2S 

30 

9. 

10 

11. 

12. 

13. 

14. 

15. 

16. 

5 

10 

12 

27 
-9" 

15 

48 
~6~ 

39 
-3" 

40 

7 

16 

nr 

33 

~8~ 

22 
~3~ 

24 
-5~ 

70 
1  2 

75 

"8" 

50 

T¥ 

9 

14 

_2~ 

40 
"7 

50 

1  7 

~S~ 

42 

~8~ 

80 

-7- 

60 
1  1 

12 

-4~ 

21 

~4- 

54 

45 
1  1 

25 

60 
T¥ 

83 
"9" 

70 
T¥ 

1  1 

36 

nr 

19 
"3" 

19 
2 

23 

"7" 

35 
~3 

58 
~5~ 

80 

13 

18 
~1~ 

1  7 
"3~ 

20 
-3~ 

38 

28 
~5~ 

43 
~4~ 

90 
"3" 

Note.  In  actual  business  operations,  improper  fractions  are  rarely 
changed  to  mixed  numbers.  The  fractions  above  are  as  large  as  are 
ordinarily  met  with  in  the  business  affairs  of  life.  The  work  which  fol- 
lows is,  however,  valuable  for  mental  drill. 


17. 

150 
T2- 

95 
"3~ 

132 


18. 

200 


95 

nr 


105 
"T5~ 


19. 

w 

125 
TOT 

87 
"3" 


20. 

200 
"25- 


150 

135 
"10 


21. 

124 


500 
"25- 


75 
T5 


22. 

100 


100 
100 


23. 

132 


65 
T3 


12  1 


62 


COMMON  FRACTIONS     REDUCTION 


Change 


1. 

To  halves : 

3,    6, 

2,      7, 

5, 

9, 

12,      8, 

10, 

4 

2. 

To  sixths : 

7,    4, 

8,      2, 

10, 

3, 

5,      9, 

6, 

7 

3. 

To  eighths : 

8,    3, 

5,    12, 

7, 

6, 

9,      2, 

4, 

10 

4. 

To  fourths : 

9,    6, 

2,    10, 

3, 

5, 

12,      7, 

4, 

8 

5. 

To  tenths : 

5,    7, 

9,      2, 

4, 

6, 

3,      8, 

10, 

12 

6. 

To  thirds : 

6,    4, 

2,      7, 

5, 

3, 

12,      8, 

9, 

10 

7. 

To  sevenths : 

4,    3, 

7,      6, 

8, 

5, 

2,    10, 

12, 

9 

8. 

To  ninths : 

2,    9, 

3,      5, 

6, 

7, 

4,      8, 

11, 

12 

Ghi 

inge  to 

improper  fractions : 

9. 

H, 

2*, 

8+, 

°2> 

7+, 

4+, 

6ft, 

9+ 

10. 

Q2 

12*, 

8|, 

llf, 

10-?, 

Q8 

12*, 

4f 

11. 

6#, 

5ft> 

8f, 

n, 

12*, 

H+, 

6T52, 

Q2 
"3' 

11* 

12. 

8A, 

16*, 

6ft, 

20*, 

io+, 

2ft 

i    2% 

Q  9 

5f 

13. 

Hi, 

9ft, 

1     1 

9  9 

30f, 

50+, 

xu8> 

8-S. 

°9> 

12+ 

14. 

15i, 

12f, 

4ft, 

20*, 

6+, 

9*, 

74 
1  7? 

°To, 

2t3t 

15. 

6^- 

U5> 

8ft, 

12*, 

25*, 

3f, 

&*, 

7_5_ 
'  1  2, 

22+ 

16. 

1  1  2 

13+, 

20f, 

33^-, 

16|, 

8-g-y 

6+, 

12+, 

8f 

Note.  See  note  on  page  61,  which  applies  also  to  the  changing 
of  mixed  numbers  to  improper  fractions,  and  to  the  work  on  this- 
page. 


17. 

25*, 

15+, 

75+, 

60ft, 

12ft, 

40*, 

50*, 

30ft 

18. 

50f, 

12ft, 

18+, 

20*, 

26*, 

30+, 

75+, 

.60+ 

19. 

40*, 

80+, 

100+, 

16*, 

18ft, 

21+, 

40+, 

26* 

20. 

37+, 

62+, 

90+, 

80+, 

70*, 

60+, 

100+, 

45+ 

21. 

50ft, 

40+, 

30*, 

20+, 

42+, 

15*, 

30ft, 

70+ 

22. 

10ft, 

12ft, 

35^, 

100*, 

10ft, 

21*, 

12ft, 

90ft 

23. 

75+, 

40*, 

75*, 

90+, 

16+, 

22+, 

150+, 

12++ 

24. 

55+, 

lift, 

50*, 

200+, 

14f, 

17+, 

20*, 

Hft 

COMMON  FRACTIONS  REDUCTION  63 
Express  in  lowest  terms  : 

12           3           6         _5_         2.        _7_  3.  _2_  _9_  _3  _4_  2_  _4_      _2_  _1_2 

■■       T?      T2J       8?       105       6?       145  9?  10?  12?  21?  14?  16?  18?     20?  20 

9          6.        _6_        4_        A           3.        _4_  10  _8_  _3_  _5_  _6_  _6_  _8_      _5_  .14. 

■•        9?       12?     10?       8?         6?       16?  12?  24?  18?  25?  14?  16?  18?     20?  20 

3          6           4         _9_      _8_      _8_      _6_  _2__  12  _4_  _8_  1.0.  10  10      _6_  _16 

•      TO"?       6?       18?     12?     10?     18?  12?  18?  20?  16?  14?  16?  18?     20?  2  0 

A.       _4_      JLQ.      _6_       16       _3_       1.8.  _5_  JLJ2  J_0.  J_j6  JUL  19  Li.      JL.  JUL 

■•      12?     30?     24?     20?     15?     24?  15?  24?  15?  24?  14?  16?  18?     20?  2  0 

K          2.       _2         IS       JL      _6_      JLO  _4_  15  _7_  1.4.  9_  14  16       1_0  6 

u*        8?       11"?     15?     24?     15?     2  5?  24?  18?  21?  21?  T5?  16?  18?     20?  2T 


60?  45?  32?  45?  70?  75?  36?  72?  48?  36?  64?  30?  45?  63 

7  JUL  3.2.  jj.  0.  JJL  2.0.  6.0.  4.5.  2.2.  2^4.  3.6.  48  20  42  56 

■•  40?  48?  75?  72?  45?  75?  55?  33?  48?  48?  64?  30?  "45?  6"3" 

ft  JL8_  19,  _2_  JL8_  2  4  4_2  3_0  1_5  XA.  ^_  4_0  J. 4.  3_5  SI 

°*  27?  30?  48?  60?  64?  60?  50?  50?  28?  64?  64?  35?  50?  63 

Q  JLO  .18.  3.6.  1.2.  1_6  2_5  XA  3.3.  16  5_0.  5_6  2.8.  5  0  18 

**  60?  45?  72?  84?  80?  40?  49?  88?  75?  75?  64?  35?  60?  81 

in  2_0  JJL  _9_  3.5.  3_0  14  4_5.  7^2  IS.  3J2-  12  _25_  4  0  A5 

xv*  80?  96?  81?  56?  54?  63?  50?  80?  39?  40?  64?  35?  64?  ¥T 


1  1           25           IS           60         _5_0_         1  6         _2_0_      _1_5_  _2_4_  4  8           3_0  6  0 

■L-L*      100?     132?     180?      2  00?     160?     180?     18  0?  "120?  108?  125?  T5  0 

1  9       _2_5_         75           8  0         _9_0_         36         _5_5_      _7_2_  _6_  _60_  _6_0  9  0 

**•       125?     150?     120?     100?     144?     110?     144?  100?  108?  125?  150 

1  Q          4  0            3  2            66  ,       ,  2  5            30         _A2_         18.  _2  4  84            50  24 

±0*      200?     120?     132?     175?     110?     126?     260?  144?  108?  T25"?  T"5"I) 

1  A       -J-J-        3  0         _2_5_      _4_5_      JJ           6  0_         3_0_  120  36           75  15 

x**       132?     100?     225?     135?     165?     240?     180?  T80?  108?  T25"?  T5"0 

IK        120        110        125        150       .1.20.      1.0_0        140  110  1  00  100  100 

*v'       150?     130?     200?     175?     360?     250?     210?  330?  108?  125?  150 

Is  it  sensible  to  divide  by  the  largest  possible  number?  What 
reason  can  you  give  for  your  answer? 


64  COMMON  FRACTIONS     REDUCTION 

Change  to  higher  terms : 

1. 
2. 
3. 

4. 


5.   To  twentieths : 

1131234  1  3  7 

2)        4>        4>        5)         5>         5)        5)       TO)       TO)       TTT 


1 

2) 

1 

3;' 

2 
3> 

1 
4> 

3 
3? 

2 

4? 

1 
5) 

3 

4) 

1 
6> 

3 

1 

2 

2 

4 

5 

4 

2 

2 

1 

3 

7> 

5> 

■6> 

4> 

f> 

6> 

8> 

7> 

8> 

5 

3 

4 

5 

3 

4 

1 

4 

1 

3 

5 

7> 

5? 

"6> 

8) 

7? 

10J 

8? 

"9? 

9> 

9 

6 

7 

2 

3 

7 

6 

5 

5 

6 

7 

7> 

9> 

9? 

10? 

8; 

9> 

TU> 

8) 

8> 

TTT 

6.   To  twenty-fourths : 


1235357  1  5  7 

21        3)        4 j        6)        8  J        8?        8?        T2">        121       T"2" 


7.   To  thirtieths : 


121415  3  9  2  11 

2)        3)         5>         5>        6)        6>        10)        TO)        T5>        TIT 


8.   To  thirty-sixths : 


1  2  3  _5  2.  5  7  11  1  5 

2>         3)        4)        6)        9>        9)        T2J        T2)        T"8>        T8" 


9.   To  fortieths: 


1324171  9  1  7 

2  f        4)         5)         5)        8)        8)        10)         10)        "2~0>        "2  0" 


10.   To  forty-eighths : 


1  2  3  _5  3  5  5  7  1  1 

2)        3)        4?        6>        8)        8?        T2>        T2>        T6>        2T 


Change  to  a  like  denominator : 

11.                               12.  13.                               14. 

f  and  I  -3%  and  f  \   and  ^  T7^  and  f 

^  and  ^  ^  and  f  f  and  ^  T5T  and  f 

TV  and  -fo  ^  and  f  ^  and  f  ■&  and  % 

T\  and  f  ^  and  J  -^  and  f  &  and  «£r 

f  and  I  T\  and  T5¥  i  and  ^  T%  and  H 


COMMON  FRACTIONS     REDUCTION  65 

Change  to  their  least  common  denominator : 

1.  J  and  \  2.  i  and  -f     3.  J  and  |     4.  J  and  ± 

|  and  J       J  and  J        £  and  §  £  and  -f 

J  and  J       |  and  |        |  and  £  £  and  £ 

J  and  §       J  and  \  J  and  £  -J-  and  \ 

\  and  J       \  and  J        i  and  £  i  and  £ 

J  and  i  i  and  J        \  and  J  J  and  J 

J  and  £       J  and  \  \  and  J  \  and  ^V 

i  and  f       i  and  TV       J  and  \  \  and  £ 


|,  i  and  i       6.  §,  i  and  J      7.  i   J,  and  TV 

i  h  and  J  J,  i  and  \  \,     \,  and  ^ 

i  i  and  J  §,  ^  and  i  i,  J,  and  iV 

|,  |,  and  J  |,  i  and  \  #,  },  and  § 

h  h  and  i  i  i  and  £  J,  J,  and  ^ 

i  i  and  i  i  |,  and  J  J,  TV,  and  i 

i  i  and  TV  J,  J,  and  J  i,  J,  and  i 

i,   i  and  J  §,  £,  and  TV  TV,  i  and  J 


f  and  J    9.  Jandf    10.  f  and  f    11.  §  and  f 
|  and  |      f  and  ±       f  and  f        f  and  § 


f  and  f  ^  and 


3  wiu  5  f  aiiu  3  ¥  anu  f  -j^  ana  f 

f  and  f  f  and  f  1  and  f  f  and  T% 

f  and  |  f  and  f  I  and  f  ^  and  f 

f  and  f  f  and  f  f  and  f  ft  and  J 


68 

COMMON  FRACTIONS  .  ADDIT 

ION 

l. 

21  +  1 

2.     7i  +  If 

3.        8f :.+  f 

4. 

3*  +  * 

H+H 

21  +  1 

f+3f 

7f+l| 

ii+i 

3f  +  i 

7f+lf 

f  +  5f 

21  +  41 

6  +  5f 

l*  +  2* 

4f+H 

I +  6| 

3,11 

5  T  ±S 

*8  +   8 

^To  +  TV 

U  +  i 

<§'+* 

5s  +  "8 

To  +  8ro 

31  +  1 

5f+U 

2|+1| 

'A  +  i-A 

5  +  21 

101  +  2| 

I  +  6J 

io«  +A 

6. 

6j  +  * 

6.     8*  +  f 

7-      3f  +  * 

8, 

41  +  21 

61+1 

41  + A 

7|  +  | 

71  +  1J 

41  +  1     . 

10i  +  i 

9*+! 

121  +  31 

io*+t 

5*  +  * 

2i  +  f 

91  +  41 

41  +  tV 

^6   +    3 

io|  + A 

61 +  7^ 

2l  +  TS 

OS   T   4 

8   3     j_    2 
8TTT  X   5 

101  +  31 

6*  + A 

1tV  +  ! 

6f  +  f 

81  +  41 

51  +  tV 

5*  +  ! 

1A  +  1 

15A  +  51 

Add: 

9. 

10. 

11. 

12. 

13. 

14. 

14f 
_3J 

20| 
_5£ 

15f 
101 

10* 
_6| 

24f 
8| 

30* 

45f 

m 

.    501 

_5i 

421 
12j 

64f 
6f 

18* 
7| 

75^ 
251 

35* 
_3| 

60T\ 
17| 

16* 

7f 

200* 

37i 

29TV 
6| 

54^ 
HI 

COMMON  FRACTIONS     ADDITION  69 

1.  5.  9.  13. 

lil  2jl  2,5  1    l    1 

3  +   6  3-r"g"  3   +   6  2   +   3 

111  2,1  2,4  I  _l_  I 

3+T2T  3+T3"  3  +  ¥  2  +  5 

l_l_l  2__|1  2,7  i-Ll 

3  +  i  3   +   6  3    +T2-  2   +  T 

l_l_]  2..1  2,4  i-L1 

3  +  T8~  3   +  T8~  3   +  T3"  2   +   9" 

2,1  1     |      ii  1_|_1_ 

3  "T  T2  3  +  T 8  2  +  TT 


1  _L     1 
3  +  XT 


2.  6.  10.  14. 

ill 

3   +    4 


I  J-     1 

4   T    2? 


I  +  tV 


3,3 

4+8 


III  £-l-i  3,5_  4-1-1 

4   +  T"2~  4+8  4+1^  3+5 

111  3_,1  3,3  1     k»  1 

4+2  4+21T  4+T6  3+T 

111  3_,1  3     i      11  I  _|_  1 

4   +  T6~  4+2  4+2TT  3+8 

111  3,1  3.,5  Ij_l 

4  +  8  4  +  T2  4  +  "2T  3  +  TXT 

3.  7.  11.  15. 

Ill  Ail  5j_7  lil 

6  +  2  6+2T  ¥  +  TOr  4+5 

III  5,1  5_i_2  1  _L  1 

6+T-8~  6+T"2"  ^-+3  4+6 

III  III  5     I     11  Ij_l 

6+T~2~  6+3  6"  +  T~2~  4+T 

III  5_     ,     1  5     i      15  l_Ll 

6+3  6  +   2  "6+1*8*  4   +   9 

6   +  A"  6  +  TS"  f+A  4   + 


9 


1 
Tcf 


4.                                  8.                                 12.  16. 

Ill  ^_1_1  5,9  Lil 

8  +  4  8  +  T¥  8   +  TO"  8  +   5 

111  3,1  5,3.  lj_l 

8   +  T~f  8   +    3"2"  8   +   4  ¥+6 

I  _1_I  £  _l_  I  5,5  111 

8   +    2  8   +   4  8+-3~2  S+T 

i_i_i  ^.i-i  5,7  iii 

8   +  T2*  8   +    2  8+T6  5   +   6 

i  +  ^  l  +  A  i  +  ii  "+* 


68 

COMMON  FRACTIONS  .  ADDITION 

l. 

2}  +  } 

2.     7}  +  If 

3.     81  + 1 

4. 

3}  +  | 

H+H 

2}  +  i 

l  +  3f 

7* +11 

11+ 1 

3!  +  } 

71+11 

f  +  5| 

2} +  4} 

6  +  5} 

11  +  21 

4f+l* 

f  +  6| 

t  +  i* 

^8+8 

6A  + A 

ii+i 

4}  +  f 

5"8  +  5g 

A  +  8  A 

3}  +  ! 

5|  +  1} 

21+1} 

7   5        I      1     7 

5  +  2i 

10}  +  2} 

1  +  6} 

io»+A 

5. 

5}  +  i 

6.     81  +  f 

7.     3|  +  | 

8. 

4} +  2} 

6*+} 

4}  + A 

7!  +  ! 

71+1} 

4}  +  } 

10}  +  i 

9f  +  ! 

12}  +  3} 

m+t 

&i  +  t 

2f  +  | 

9}  +  4} 

4}  +  A 

°6   T    3 

io!  + A 

6}  +  7A 

2s  +  A 

81+1 

8A  +  ! 

10}  +  3} 

6}  + A 

1A+! 

6f+f 

8}  +  4} 

5}  +  A 

5i  +  ! 

i*  +  * 

15A  +  5} 

Add: 

9. 

10. 

11. 

12. 

13. 

14. 

14f 

20! 
_5£ 

15f 
10} 

10! 
_6} 

24f 

8} 

301 

45f 

10} 

.     50} 
_6} 

42} 
12} 

64f 
6f 

18| 

7} 

75A 
25} 

35* 

_3| 

60fV 
17} 

16f 

7! 

200} 
37} 

29TV 
6} 

54A 

iif 

COMMON  FRACTIONS     ADDITION  69 

1.                                   5.                                  9.  13. 

lil                                              2,1  2,5  1     .     1 

3   +   6                                            3  +  ^  3   +    6  2~|-3 

2,1  2,4  1-1-1 

3+H  3   T   9"  2T5 

2j_l  2_,7  1-L-l 

+   6  3    +12  2   T  f 


1  _L    1 

3   +   9  3 

2_il  2,4  1-i-l 

3+T8  3+T5"  2   +   9 

_1_1  2,ii  1     *       * 

+  T  2  3  +  T8  2  +  TT 


1  4-  JL 
3+18 

1  _L      1 
3   +  TS 


3  f  TS  3 


2.  6.  10.  14 

3  I       1  3.     ,     3 

4  +  T^  4+8 


1   J-     1 

4   T  -2U 

ill  ^4-1  3_1__5_ 

4   +  T"2"  4+8  4+12 

lil  3,1  3,3 

4  +  2  4  +  '20'  4   +  TB" 

111  £  4_   1  3,11 

4   +  TB~  4+2  4  +  ^0~ 

1.1  l_Ll  3.15 

4+8  4+T^  4+2T 

3.  7.  11. 

i,i 

6   +  2 


5 

+ 

? 
3~CT 

5 

f 

+ 

2 
3 

5 

f 

+ 

H 

5 

6 

+ 

15 
TS 

5 
6 

+ 

A 

111  £_!_!  5,7  l_l_i 

8   +    3"  "2  8   +    2  8+lHg"  5   +    6 

8"  +    2T  8+A  8   +  if  5+4" 


5 

8 

+ 

9 
40" 

5 

8 

+ 

3 
4 

5 

8 

+ 

A 

5 

8 

+ 

7 

is 

5 

8 

+ 

1  3 
24 

1 
3 

+  1 

1 

3 

+  i 

1 
3 

+  + 

1 
"3 

+  1 

1 
3 

+  A 

15. 

1 
4 

+  1 

1 
4 

+  i 

1 

I 

+  + 

1 

4 

+i 

1 
4 

+  tV 

1  4-  -i- 

6   +    2T 

iii  s.i 

6  +  T¥  6  +  T2~ 

1.1  5     ,     1 

6  +  T"2~  6+3 

1.1  5     ,      1 

6+3  6   +    2 

4  4-  -JL-  |j       1 

6   +    2T  6   +  TS 


4.  8.  12.  16. 

Ill  £_l_l  5,9  1_l1 

8   +   4  8  +  T  6"  8    +  TO"  8   +    5 

1_I_1  3j_l  5,3  1_1_1 

8   +  T6~  8   +  T2"  8   +    4  8"  +   6 

1.1  1_1_1  5,5  1.1 

8   +  2  8   +   4  8   +   3"2  S+T 


70  COMMON  FRACTIONS     SUBTRACTION 

1.  2.                                   3.  4. 

2-i  7-1  15-4|  2.wif 

3  -  f  5-|  12-2*  3- If 

4-|  12 -A  4- If  7-5} 

6-|  20  -  |  10-3f  10-3f 

9-|  10 -f  6-4tV  8-2* 

8  -  f  12  -  |  7  -  5f  5  -  If 

7-i  25  -A  5 -If  11  -  4f 

5-^  6-f  9-3|  12-2^ 

2-^  8-f  4- If  2- If 


n- 

1 
8 

2i- 

1 
4 

7i  _ 

1  2 

1 
10 

Q2 

^3 

1 
2 

4|- 

1 
8 

6f- 

1 
6 

5f- 

1 
2 

8f- 

1 
"3 

6.  7. 


5i- 

-3} 

6f- 

-If 

10}  - 

-4f 

12* - 

-2} 

8f- 

-5f 

71- 

-2f 

20*- 

-M 

11- 

-1} 

811  ^2           2 

3    ~    4  '  3    ~"    5 

Q6           1  OH   9             1 

°T  —   2"  zuTo   T   3 

101  _  l  n|  _  i 

6f-i  12}  -J 

11           3  1A2              3 

4e  —  4  -10  3  —  TOT 

Kl           1  C   8             1 

°2~    5  °T5    —    2 

12}  -  }  40|  -  T\ 

44    _   1  OE1    _     3 

^T         3  *D2         TT 


Subtract : 

9.                    10.                   11.  ,  12.  13.  14. 

14                25J               50  *36f  40  28 

O4                             85                             ""8  ^2  O3  7jg 

42  37*  14f  44 


6? 


T5 


100      100      100      100       100       100 
37J      12J      33|      66f       87J      _62| 


COMMON  FRACTIONS     SUBTRACTION  71 


12  5 

3  _3 


8  2 

T5    ~    5 


2.         2    —    4  3. 


3  1  11  3.   _    1 

4  ~~ '4  2    —    6  42 

13  I!  1   _    1 

8    —  8  3    —    6  63 

9               4  1 1  2    _    1 

TO"  ~  10  312  36 

4  2  11  5  1 

5  —  5  2    "~    8  82 

6  5  I 1__  1   _    1 

T  7  6           12  8           4 

7  3_  1  _    1  _3 I 

TO  10  3           9  10            5 

11   _    S  I 1_  X  _  i 

T2  12  2            10  9            3 


5  4  3  G  X  5     *  7 

•  5    -    4  b«  8    -    6  •• 


T6-  - 

8 

3 

7 

2 

If 

8 
T5 

1 
2 

1  1 
T  ¥ 

9 

1  "0 

7 
T  6^  ~~ 

1 
3 

7 

2 

7 

9 
10 

7 
8 

6 

7 

1 
6 

7 
T6"  ~~ 

5 

T2 

7 
9 

7 
8 

8 
T3 

1 
2 

5 

7 

2 
1  1 

9 
10 

5 

6 

T  2    ~ 

6 

8 
9  ~~ 

2 
3 

3 

4  ~ 

5 
16 

3 
10 

3 
20 

5 
14 

2 

7 

3 

5 

3  fi75*  »742  ft  5! 

~    -    3  O-  T   -    2 


25  23  6_1  5_1 

3  _   T  2  5"  —   TO  T2  83 

5.5  61  32  3._I 

6    —  T2^  T  —    3  4    —    3  73 

33  51  3_1                                       H 1 

T  —  TO"  "92  54  128 

5  4  9             4  I   _    2.                                   _7 2 

6  —    5  TO    "5  27  103 

32  53.  22  74 

4  —    5  6    —    4  3    —    5  8    —    5 

72  85  31  52 

8    ~    3  ¥—    6  4~6  8    —    5 

112  71  71  12 

T2    ~    3  TT"~    2  T0~2  2    —    9^ 


9.      e-f  10.    T\-i  11.      f-  i  12. 


5 
T  2    ~ 

1 

5 
1  6 

1 
3 

7 
9 

7 
10 

2  1 
30 

4 
1  5 

7 
1  2 

3 

8 

1  4 
1  5 

5 
6 

9 

20  - 

1 

s 

72 


COMMON  FRACTIONS     SUBTRACTION 


1  1 

2  —    4 

5. 

3             1 
8   —  TO* 

1  1 

2  12 

3             1 
8    —  T  6 

1  1 

2  —    8 

3            1 

8    —    2T 

1  1 

2  -  TU 

3           1 

8    —    4 

1  1 

2  —   6 

3             1 
8   -  -3"2- 

9. 


13. 


5 


1 1 

"2T 


TOT 

3 
■3"2" 


1 
T 


i-A 


1       1 

3    —    6 

6. 

2  1 

3  —  -9 

10. 

2           4 
3-9 

1             1 
3  —  T3" 

1        1 

S  -  T8 

2  7 

3  —  T5" 

I         1 
3~9 

2.           1 

3      n 

2  5 

3  —  T  2" 

1           1 

3   —  T"8~ 

2  1 

3  —  6 

2  11 

3  —  T8~ 

1 1 

2  1 

3  -  T^ 

2  4 

3  —  3T 

id    i  -  i 


x      1 
3  ~  ny 


1 

T 


1-1 

i  _   l 

3   -  "g- 


0      I  1 

*•      4   -  Tl 


T"g- 


7       3  1 

'•     4  —  T2- 


11.  I- 


15.    i-i 


1        1 

4  —  ^TT 

3           1 
4~2 

1         l 

4~8 

3  1 

4  -    21F 

I          1 

4    —  T2~ 

3  1 

4  —  rg- 

1             1 
4   —    2T 

3           1 

4~8 

2V 


5 
T6 


A 


7 


1 

Ta 


1 

T 


4.    i- 


1       1 

6    —  T  8" 

8. 

5  1 

6  —  T  "2 

I            1 
6  —  "51T 

s          1 
6    -  -30- 

1        1 

6    —    2T 

1            1 

6   —  T8" 

1             1 
6   —  T"2" 

5  1 

6  -  -g-g 

1            1 
6   —  TST 

1            1 
6   -  "ST 

12.  I 


5 
T2" 


TF 


2 


4 


16.    i-i 


1 

5 

- 

l 
8 

1 
2 

- 

tV 

1 
6 

- 

1 
9 

l 
5 

- 

tV 

1 

T 

— 

1 
8 

ADDITION  AND   SUBTRACTION  73 

1.  *  plus  *  2.   \  +  *  3.  A  and  *            4.     {  +  f 

1  locc      1  2           1  9       lpoa  1  7    _    2 

2  ieSS      2  3    —    2  Ta    iebb  5  "5"           3 

!  plus  J  I  +  i  I  and  J  A  +  i 

2  lot2t2      1  3    _    1  7     1p™  3                                 _5 1 

3  iebb     6  4           2  8     1Utofe  4  12           4 

}  plus  f  |  +  *  |  and  J  TV  +  f 

*  *—  I  t  -  I  I  less  J  A  -  I 


|  plus  f  |  +  1  A  and  I  T9e  +  f 

5  loac      2  5  1  9       1PQQ     1  9      _    1 

6  ieSS     3  8    ~~    2  TIT    iebb     2  T6  8 


I.  7j  +  l  6.       2  + If  7.     11  +  !  8.   18+1A 

7*-*  2-1*  If  -  f  18-l^r 

10  +  3*  5|  +  i  15|  +  1  9*  +  * 

10  -3*  6f-|  15i-i  91-1 

Oi     I     I  15,2  74      i      1  ^1_|_1 

O5   T   2  J-G     1      3  *T  T   2  °3   "T   6 

841  152  74          1  Qll 

5~"2  x6—    3  'T  ~~    2  °3    ~~    6 

3|  +  |  12* +  f  4^  +  |  5|  +  i 

Ql          1  lOl           3  A    3            1  K5           1 

^4   ~    8  1Z2    ~"    5  ^TO           5  °8   —    4 


Add,  and  subtract : 


20* 

_Zi 

10.  50* 
12| 

11. 

18* 

_8* 

12. 

37f 

13. 

44* 
10* 

14.  13* 

75* 

40| 
20* 

65| 
10* 

16* 
_2* 

48* 

19f 
_9* 

37* 
12i 

12i 

66| 
33* 

33* 
16* 

87* 
12* 

83* 
16| 

74  COMMON  FRACTIONS     MULTIPLICATION 

Give  products : 

1.  2  X  |      2.  4  X  i      3.   2  X  T5T     4.   8xf 


3 


9xf  8xf  4xTV  4x 

3xf  7x|  6xf  9x 

4  X  f  6  X  |  9  X  T3T  2  x  | 

7x|  2X|  7xf  3X| 

5X6  «  X  i"o  0X4  0X4 

8xf  9xf  8xj  6x| 

6xf  5xf  5xf  7x^ 


5.    10  X  |  6.      7  X  4.  7.     2  X  ft  8.      25  X  i 

12  x  f  8  X  H  8x|  32  x  i 

8XA    ■  9xf  5xf  40  X  f 

7x|  10  xf  3xf  28  X I 

10x|  11  Xf  6xi  45x* 

9  X  f  12  x  I  9  x  A  50  x  tV 

12  X  f  20  X  f  7  X  f  36  X  i 

11  Xf  14xf  4X^  44  Xi 


Solve  by  cancellation : 

9.   28  X  f  10.    84  X  A          "•   50  X  ^          12.     60  X  U 

18  X  I  15  xi  24  x  ^  20  xf 

44  x  T5T  42  X  f  45  X  I  64  x  f 

75  x  A  90  x  i  36  X  i  70  x  TV 

20  x  A  27  Xf  80xTV  72  X  A 

21  xf  35x4  48  X  A  40xf 
30  x  I  96  x  H  32  x  I  56  X  f 
66xT8T  49  Xf  81  X I  100x-285 


COMMON  FRACTIONS     MULTIPLICATION  75 

Multiply: 

1.  2.  3.  4. 

H   by  3  4T3o  by  2  2|  by  3  61  by  8 

4|  by  5  7J  by  5  3|  by  4  121  by  4 

61  by  4  21  by  7  5i  by  8  9f  by  10 

2f  by  2  5T2T  by  4  If  by  5  3f  by  8 

8t2t  by  5  9i  by  8  4|  by  6  5|  by  6 

3|  by  4  4f  by  3  2f  by  4  If  by  12 

7-|  by  7  31  by  4  81  by  5  41  by  9 

51  by  4  10A-  by  2  lOf  by  3  11 J  by  6 


5.  6.  7.  8. 

41  by  5  31  by  10  2f  by  4  81  by  7 

3|  by  6  7§  by  9  3f  by  5  121  by  5 

2}  by  7  121  by  5  4f  by  7  4|  by  8 

51  by  9  61  by  8  3|  by  5  2f  by  6 

10|  by  8  21  by  11  5f  by  3  10J  by  9 

61  by  10  4TV  by  15  6J  by  9  3f  by  10 

8A-  by  11  81  by  7  4f  by  9  81  by  11 

91  by  12  91  by  9  3f  by  7  5T\  by  4 


9.  10.  11.  12. 

20TV  by  5  9T2T  by  20  10|  by  9  11  by  12 

4f  by  12  4TV  by  11  18f  by  5  51  by  16 

16f  by  5  8f  by  40  40f  by  4  21  by  18 

4f  by  20  6f  by  15  21f  by  4  6TV  by  20 

6^  by  25  2|  by  30  60f  by  2  5T\   by  15 

8f  by  12  3f  by  25  .  25|  by  6  4f  by  21 

4f  by  16  51  by  20  221  by  3  131  by  3 

15|  by  5  7f  by  14  50^  by  5  371  by  2 


76               COMMON  FRACTIONS  MULTIPLICATION 

Find  products,  cancelling  when  possible : 

1.     i  dt  f  2.      \  of  f  3.      i  of  |            4.      §  of  f 

1  y  8  ^  y  5-  Av6  3wl 
4  A  ¥  8  A  6  3  A  7  4  A  8 
A   y      8  2    y    3  5VX  5    v      9 

2  A   TT  T  A    4  7    A   T5"  "9    A    2~a 
4    y    3  1    y   A  2    y    7  3    y      8 
T  A    8  2    A    2  ¥  A    8  8    A  Y5 
2w9  A   y    1  *■  V   4  2    y      5 

3  A  TO  8    A    5  4    A    5  y  A    2"^ 
A   y    2_  5    y    3  4    v      1  3      v    5 

4  A  3  ¥  A  8  9  A  T  2"  TO  A  ¥ 
2w3  3  y  A  iv8  2  y  5 
5*4  T  A    6  2    A    9  lT  A    8 

5  y  3  A  y  10  6y2  A  y  A 
¥  X  T¥  5   X  TT  TT  X    3  3X4 


5.  0f  AA 
7  U1  3  5 

6  JL  nf  -7- 

D-   11  U1  12 

7.   |  of  A 

8.   f  of  f 

1  V  -1- 

5  A  11 

5   y   3 

TT  A  Ta 

5  y  6 

9  X  7 

6   y   5 
TT  X  36 

1   y  12 
8  A  63 

i  V  1  2 
6  X  "2  5- 

2  y  2  1 
7  A  TO" 

4  v   6 

5  A  TT 

1  1  y   7 

TT  A  33 

2  A  8 

7   y   8 
"24  A  TO 

1  5  y  1  6 

32  A  22 

5  v   3 

6  A  2T 

6  y   7 

7  A  1  5 

10  y  3 
TT  A  5 

1  Y  12 
4  X  2T 

4  y   71 
¥  A  16 

8  y  1 
TT  A  4 

9  y  5 
10  A  7 

10  y   7 

11  A  20 

4  y  8 

T  X  9 

3  y  4 

20  A  15 

2  1  y  1  1 
22  A  14 

14  y  3 
T  5"  X  y 

8  y   5 
10  A  32 

5   y  6 
1  2  A  7 

3  y  10 
40  A  TT 

1  2  y  9 
TT  A  TTF 

Comparison  of  Fractions 
9.   Which  of  the  following  fractions  equal  one-half? 

ft       _6_        1       A       JL        4.       2        _4_        3.       _5_       _7_       XJL 
8>      12?      5?      9>      4?      7>      8J       10>      6>      10'      15?      20* 

Which  are  greater  than  \  ?     Which  are  less  ?     How  can  you  tell 
at  a  glance? 


10.   Which  of  the  following  fractions  equal  one-third? 

A.        3.       Jl  3         3        _6_  4_  IS  2.       _6_        2        _J_ 

11     "9"?     T2J      4>      8?    -15?     T2>      1"8~>      6>      18?      5>      20' 

Which  are  greater  than  §  ?     Which  are  less  ? 


COMMON  FRACTIONS     MULTIPLICATION 


77 


Find  products,  cancelling  when  possible : 
i 


1. 

H  X  f,  or    f  X  ! 
21  X  f ,  or    i  x  f 

4|  X  i  or  f  X  1 
If  Xi  or  {Xf 
3*  X  f ,  or  J£  x  | 
o^  X  y>  or  -j-  X  y 
2|  X  J,  or  f  X  I 
6i  X  f,  or  V-  X  I 


2. 


I  X    2f,  or     I 

TT  X      3y,    or   TT 

4|,  or    I 


x-1/ 


x-¥- 


8.  v      4-^ 

9   A      ^8; 


{  x    2| ,  or     f 

f  X    6i  or 

t  X    5J,  or 

i  X  12f ,  or 

I  X  10i  or 


22 

7 

V  35 

x  nr 

V  17 
X   "  6" 

V  49 

X  ~3~ 

V  25 

V  8  1 


If  x 


3f 


*fX     If 

8j  X  1* 


Hx 


Oy   X        «->2 

71  X  41 
3*  X  4* 
64- X    li 


3. 

or  V  x  J£ 

or  -3/  x  -V- 

or  %«  X  ii 

or  fxV 

or  -y-  x  J 

or  -V-  X  f 

or  -V-  X  « 

or  -2/  x  f 


If  X  10|, 

5|X    11, 

4AX    If 

2|X    21, 

1  -3_   V    ^    3 

xl  l   A  o10, 

91  x    6f 

iiixiTV, 

61X1*, 


or  -V-  X    I 

or||X    ! 
or  V  X  V5 

nr     14    v    33 

0r   TT  X  TO 

or  -2/  x  -4/ 
or  V-  X  If 

5  5    v    14 
"9"  x  TT 


or  %5- 


Multiply : 

5.   45 

6.    16 

7.    24 

8.    15 

9.   21 

10.   40 

_2| 

_4| 

9-5- 

^T2 

M 

42 
^3 

_5| 

50 

32 

75 

60 

35 

80 

_8f 

Jf 

42 
^3 

95 

93. 

_M 

25 

30 

18 

22 

14 

20 

_M 

_M 

_2| 

Ji 

Jk 

12} 

78 


COMMON  FRACTIONS     MULTIPLICATION 


Give  products : 

1. 

2. 

2X| 

7x24 

3|  X  4 

10X3| 

1  of  5 

«  of  A 

If  X6 

44x44 

5. 

6. 

f  of  12 

40X  + 

11x24 

f  of  10 

02    X    4 

4  of  45 

2|x3 

3X33J 

lV 


4  of 

3i  X  4 
f  of  20 

at  x  ttf 


10. 


4 
5" 

of 

15 

2| 

X  12 

3 
5 

of 

3 
5 

3. 

124  x  2 
4x64 
84  X  3 
4x24 


6ix2 


7. 

2f  X2| 

20  xf 

111  X  2 

1   V    3 
4    *    5^ 

11. 

3X  12| 

3  A  y 

16f  x3 

4x24 

4. 
A  of  f 

14x14 

8Xf 
5x3| 


8. 

14  Xf 
9x2tV 
I  of  1 

TO    X    4 

12. 

61 

1 

2  0 

81 

X2 
of  100 
X6 

50  X 


13. 

124x5 

14  x  10 

7xA 
fx24 


17. 

3X51 


of 


14. 

5x94 

7x121 

-h  of  100 

,6|X6 

18. 

4  of  ioo 

34x3 

1    v    8 

15. 


50x2§ 


of  2 


\  of  100 

6i  X  8 

2x33| 

9xf 

19. 

f  of  81 

TV  of  100 

2|X5 

6x  12i 

16. 

I  of  56 

10  X  A 
|  of  100 
13  Xf 


20. 

124  x  8 
84x9 
4x  121 
4  of  45 


FRACTIONAL  PARTS  OF  NUMBERS  79 

What  is 

1.  2.  3.  4. 


\  of  18? 

i 

10 

of    30? 

2 
3 

of  12? 

i  of  27? 

1 
11 

of    55? 

3 

4 

of  16? 

i  of  40? 

1 

12 

of    48? 

2 
5 

of  20? 

i  of  35? 

1 
T5 

of    60? 

3 
5 

of  15? 

i  of  42? 

1 
2  0 

of    80? 

4 
5 

of  50? 

\  of  49? 

1 
25 

of  100? 

5 
6 

of  12? 

i  of  32? 

1 
40 

of    80? 

2 

7 

of  14? 

1  of  45? 

■h 

of  100? 

3 
7 

of  21? 

5. 

6. 

7. 

f  of  48? 

3 
5 

of  55? 

3 
10 

of  50? 

f  of  64? 

3 
4 

of  40? 

A 

of  84? 

i  of  90? 

5 

8 

of  96? 

3 

7 

of  77? 

T3T  of  44? 

3 

8 

of  48? 

4 
9 

of  45? 

T\  of  48? 

5 
6 

of  72? 

7 
TO" 

of  40? 

|  of  27? 

7 
8 

of  56? 

7 
T2" 

of  36? 

•f-  of  42? 

4 
5 

of  35? 

4 
5 

of  60? 

f  of  33? 

2 

7 

of  49? 

2 

TT 

of  55? 

9. 

10. 

11. 

|  of  140? 

A 

of    96? 

l 

2 

of  1240? 

4  of  108? 

9 

20 

of  100? 

1 
4 

of    408? 

A  of  132? 

A 

of  100? 

1 
'      5 

of  2000? 

TV  of  144? 

8 
T5 

of    90? 

1 
3 

of    612? 

|  of  180? 

A 

of  150? 

1 
7 

of    721? 

A  of  200? 

5 

8 

of  160? 

1 
8 

of  2400? 

T7T  of  110? 

A 

of  130? 

1 
6 

of    486? 

A  of    75? 

2 
3 

of  144? 

1 
9 

of    405? 

4 
7 

of    7? 

5 

7 

of  28? 

6 

7 

of  70? 

3 

8 

of  24? 

5 

8 

of  40? 

7 
8 

of  16? 

2 
9 

of  18? 

B 

9 

of  45? 

8. 

f  of  56? 
A  of  80? 
•A-  of  22? 

|  of  72? 

f  of  32? 

f  of  63? 

|  of  40? 

f  of  42? 


12. 

i  of  45? 
i  of  70? 
I  of  50? 
i  of  62? 
J  of  31? 
£  of  80? 
|  of  25? 
i  of  40? 


80 


FRACTIONAL  PARTS  OF  NUMBERS 


1. 

2  is  J  of  what  number? 

10  is 

2. 

^q  of  what  number  ? 

4  is  i  of  what  number? 

6  is 

4  of  what  number? 

6  is  J  of  what  number  ? 

8  is 

J  of  what  number? 

8  is  J  of  what  number? 

9  is 

-|  of  what  number  ? 

5  is  J  of  what  number? 

12  is 

|  of  what  number  ? 

10  is  \  of  what  number? 

7  is 

^  of  what  number  ? 

9  is  \  of  what  number? 

11  is 

J  of  what  number? 

3  is  J  of  what  number? 

9  is 

iV  of  what  number? 

12  is  \  of  what  number? 

15  is 

|  of  what  number  ? 

7  is  \  of  what  number? 

25  is 

J  of  what  number? 

3. 

12  is  f  of  what  number? 

40  is 

4. 

f  of  what  number  ? 

6  is  §  of  what  number? 

36  is 

T%  of  what  number? 

8  is  \  of  what  number  ? 

25  is 

|  of  what  number? 

15  is  f  of  what  number? 

42  is 

f  of  what  number? 

10  is  §  of  what  number? 

60  is 

T52-  of  what  number  ? 

20  is  f  of  what  number  ? 

35  is 

|  of  what  number? 

18  is  f  of  what  number  ? 

49  is 

■£$  of  what  number? 

9  is  f  of  what  number? 

30  is 

f  of  what  number? 

14  is  §  of  what  number? 

24  is 

f  of  what  number  ? 

16  is  \  of  what  number  ? 

21  is 

|  of  what  number? 

5. 

\  of  12  is  f  of  how  many? 
f  of  how  many? 
f  of  how  many  ? 
f  of  how  many  ? 
f  of  how  many  ? 
|  of  how  many  ? 


6. 


\  of  48  is 
\  of  30  is 
f  of  60  is 


f  of  16  is  f  of  how  many? 
§  of  20  is  f  of  how  many? 
f  of  35  is  f  of  how  many  ? 
f  of  36  is  f  of  how  many  ? 
|  of  80  is  §  of  how  many  ? 
|  of  27  is  f  of  how  many  ? 


COMMON  FRACTIONS     DIVISION  81 

2  +  i  2.  2  +  1  3.   6  + J      4.  4  +  | 

4  +  1  5  +  £  3  +  1  5  +  f 

3+|  2+|  5+|  4+1 

2  +  1  4+i  3+i  6  +  i 

4+i  3+|  2+1  4+| 

3+|  5  +  1  4  +  i  3  +  | 

6+i  3+ J  2++  5  +  1 

2  +  1  6+i  6+1  5+| 


2  +  f 

6.  6  +  | 

7.      3  +  | 

8.     9  +  i 

4  +  f 

2  -  4 

*  +    6 

5  +  f 

4+f 

3  +  ! 

7  +  1 

4  +  f 

7  +  1 

3  +  i 

3  + J 

6  +  « 

8  +  f 

5  +  f 

6  +  f 

2+f 

3  +  * 

2  +  J 

5  +  f 

7  +  i 

4  +  f 

6  +  i 

8  +  f 

5  +  f' 

9^« 

7+1 

9  +  i 

8  +  1 

8  +  f 

9.      6  +  f  10.    6  +  f  11.      8  +  f  12.     8  +  | 

9  +  |  7  +  f  6  +  |  10  ♦# 

1 1     •  ■  1  fi    •      7  Q  ^.  II  Q  ^.  II 

11—    8  °   ~   T  0"  °     •      12  y     '      12 

8  +  ^  7  +  f  10  + J  7  +  | 

6+f  7+f  8+f  9+f 


7  +  f  6  +  1  7  + A  8 

8  +  1  9  +  T%  6  +  TV  6 
10  +  f                   7  + A            -       9  +  i                   U 


7 


82 


COMMON  FRACTIONS     DIVISION 


3  —   L 

1  ^  A 

4  —  ^ 


-3 


3    ~  ^ 


*  +  2 


i  +  3 

♦  +•« 
i  +  6 
i  +  3 

4  +  5 

4  +  2 

4  +  3 


8  —  t) 

*  +  4 

f+3 

4  +  5 
4  +  6 
^2 
4  +  6 
4  +  5 


4  +  2 
1  +  4 

4  +  5 
+  +6 
4  +  4 


6    ~    ^ 


5. 


t  +  2 

6.  A  +  5 

7.  |*3 

8.   f +  6 

f  +  3 

f  +  9 

4  +  6 

*  +  8 

«  +  4 

f  +  2 

1  +  2 

J7_  ^  Q 

10  •  y 

!  +  6 

*  +  3 

1  +  7 

5  _^  4 

6  ~  ^ 

3  _,_  Z 
8  —  O 

f  +  4 

f  +  5 

f  +  5 

:&  +  7 

4  +  8 

i  +  9 

4  +  2 

i  +  s 

1  +  7 

i  +  4 

1  +  3 

i+9 

J  +  6 

1  +  8 

f+7 

9. 


3   . 
TO  ~ 

12 

5  . 

8  * 

12 

7 

12 

5   . 
1  2  * 

12 

9   . 

TT  • 

12 

7   . 
9  ~ 

12 

6  . 

7  ' 

12 

7 

TT  ~ 

12 

10. 


5 

8 

7 
TIT 

5 
6 


15 
15 
15 
15 
15 
15 
15 
15 


11. 


4 +  20 

12. 

^ +25 

I +  20 

I +  25 

4  +  20 

1  +  25 

$+20 

§  +  25 

I  +  20 

f  +  25 

4  +  20 

f +  25 

|  +  20 

1  +  25 

A +  20 

f +  25 

COMMON  FRACTIONS     DIVISION 


83 


3. 


1  _^  A 

ro  •  o 
i  .  i 

t  ~  ¥ 

1  .  1 

2  ~  4 


4. 


i 
TO 


10 


1 

3 

1 
T 

l 

3 


TO  ~  5 


8. 


10 

i 


i 
TO 


9. 


13. 


10. 


i 

12 


17. 


1  .  i 

2  —  9^ 


1  .  1 
TT  ~  2 


1 
6 

1 
10 


14. 


18. 


1 

"6 
1 
3 


1 

T  ' 


l 
9 


1 
1  1 


11. 


1 
T 

1 
5 


1  .  1 

9  —  T 

1  .  I 
6  "'  2 


15. 


19. 


1    . 

7    "" 

1 
8 

1 

1 

IS  ~ 

5 

1 
TT  ~ 

1 
6 

l     . 

1 
8 

l     . 

4    • 

1 
7 

1     . 
3    T 

1 
2 

1 
TO   ~ 

1 
3 

1 
1  2      ' 

1 

9 

1 

1  1      * 

1 
4 

1      . 

7      ' 

1 
6 

1      . 

4    ~ 

1 
2 

1 

1  2      ' 

1 

6 

1      . 

8    ~ 

1 
3 

1     . 

3    ~ 

1 

1  0 

1      . 

4    ~ 

1 
11 

12. 


16. 


20. 


TT 

l 


1 
TO 


1 
TO 


1 
TT 

l 
6 


1 

1  1 


4  —  T2^ 


84  SPECIAL   ONE-MINUTE   EXERCISES 

Practice  first  for  accuracy,  then  for  speed. 

1.  Start  at  1.     Count  by  threes.     "1,  4,  7,  10,  13,"  etc. 
Record  the  number  reached  at  the  end  cf  one  minute. 
Start  at  2.     Count  by  threes.     Record  as  before. 

Start  at  3.     Count  by  threes. 

2.  In  the  same  manner 
Start  at  1.     Count  by  fours. 

Count  by  fours,  starting  successively  at  2,  3,  and  4. 

3.  Start  at  1.     Count  by  fives. 

Count  by  fives,  starting  successively  at  2,  3,  4,  and  5. 

4.  Count  by  sixes,  starting  successively  at  1,  2,  3,  4,  5,  and  6.  ] 

5.  Count  by  sevens,  starting  successively  at  1 ,  2, 3, 4, 5, 6,  and  7. 

6.  Count  by  eights,  starting  successively  at  1 ,  2,  3,  4,  5,  6,  7, 

and  8- 


7.  Count  by  nines,  starting  successively  at  1,  2,  3,  4,  5,  6,  7,  8, 
and  9. 

8.  Note.     To  follow  the  work  in  U.  S.  money. 

Starting  at  12 j,  count  by  12$ 'a  as  far  as  you  can  in  1  minute. 
Starting  at  16f ,  count  by  16f  's  as  far  as  you  can  in  1  minute. 
Starting  at  33j,  count  by  33|'s  as  far  as  you  can  in  1  minute. 

9.  How  many  of  the  following  fractions  can  you  name  in  their 
lowest  terms  in  one  minute? 


(a) 

3         4         2        3 
"6")     10)     8?     9) 

6 
T2^ 

2 

6") 

5 
10? 

6        4          3         2 

8)     6)     12)     4) 

2 
TO) 

4       6         9 

"§"?     "9?    T8" 

(*) 

4           8           8 

T2)   To")    12? 

6 
TO? 

3 
T5? 

9 

14         4           9 
2"T)    TF)    T"5") 

A, 

5          15          5 
T"5?     20"?     25? 

2  0) 

3 
2T 

(c) 

10        12         2 
1  5  J     1  ^?     1  T5"? 

10 
"25") 

12 
T"5"> 

TO) 

6         10        15 
15)     20)     30) 

20 
2"5) 

3         20        25 

T8~?    TO?     50) 

10 

40) 

6 
TIT 

(d) 

2  0        15         6 
TO"?    "2"5~?    T"8~? 

9 

27? 

7 
2"T? 

9 

6          12        11 

2T)     18?     2  2) 

5 
TO? 

2          10        12 

18)     22)     24) 

10 
12) 

14 
T6 

UNITED   STATES  MONEY 
100  cents  =  $1. 

1.   What  part  of  one  hundred  cents,  or  one  dollar,  is 

50c7?  10c7  20c7?  80^? 

25^?  5^?  40^? 


75^ 


4^? 


60  c7? 


33^? 
66^? 


85 


30^? 
70c7? 
90c7? 


2.   What  coin  equals 

25  cents? 

10  cents? 

5  cents? 


2  quarters? 
5  nickels? 
5  dimes? 


10  dimes? 
4  quarters? 
10  quarters? 


How  many  nickels 

In  a  dime? 
In  a  quarter? 
In  a  half-dollar? 
In  a  dollar? 


How  many  dimes 

In  a  quarter? 

In  a  50-cent  piece? 

In  a  dollar? 

In  a  $2.50  gold  piece? 


How  many  quarters  in  a  $5  gold  piece : 
How  many  dimes  in  a  $5  gold  piece  ? 
How  many  nickels  in  a  $5  gold  piece  ? 
How  many  half-dollars  in  a  $5  gold  piece  ? 


6.   What  part  of  a  dollar  is 

A  cent?    A  nickel?    A  dime?    A  quarter?    A  50-cent  piece? 


What  coins  will  make 

7.    50c7?          8.   40<£?  9.   20c7? 

25c7?               75<£?  SOc7"? 

30^                 55^?  60^? 


10.   70^?  11.   45^? 

85c7?  90^? 

35^?  $1? 


UNITED  STATES  MONEY 


Read : 

1. 

2. 

3. 

4. 

5. 

1.05 

2.34 

4.02 

1.12 

.90 

.25 

5.10 

10.11 

30.03 

28.07 

.01 

.08 

8.04 

5.95 

3.09 

.75 

202.45 

103.03 

20.40 

25.19 

6.84 

8.00 

20.27 

226.63 

.08 

75.00 

120.20 

305.84 

60.08 

9.02 

Add: 

6. 

7. 

8. 

9. 

10. 

11. 

$  .25 

$.16 

$  .50 

$2.10 

$5.15 

$  .42 

1.40 

.90 

1.50 

.64 

.40 

1.08 

$1.10 

$.40 

$  .33 

$1.32 

$  .75 

$2.40 

.65 

.82 

1.26 

.27 

1.75 

.13 

$2.01 

$  .39 

$2.84 

$4.0 

$2.20 

$  .64 

.67 

1.30 

.11 

.76 

.75 

1.10 

L.55  $8.25  $1.11  $1.64  $2.05  $3.30 

.42  .13  2.00  1.12  2.56  1.25 


12. 

13. 

14. 

15. 

16. 

17. 

$.23 

$.72 

$.33| 

$.54     ' 

$  .08 

$.46 

.16 

.20 

.20 

.12| 

.18 

.24 

.05 

.09 

.10 

.03 

1.25 

.02 

$.42 

$.62| 

$.40 

$  .95 

$  .82 

$.122 

.37^ 

.18 

.32 

1.06 

1.00 

.09 

.10 

.50 

.11 

.03 

.15 

.871 

&6.121         $20.30  $15.10  $1.50  $2,121  $1,331 

4.10  8.75  3.331  2.871  1.621  l-16f 


UNITED   STATES  MONEY 


87 


Finding  Amount  of  Purchases 


C8 
06 


1. 

2. 

3. 

4. 

5. 

$.05 

$.06 

$.25 

$.12 

$.15 

.01 

.09 

.08 

.07 

.07 

$.09 
.05 

$.14 
.08 

$.11 
.12 

$.17 
.07 

$.20 
.06 

$.16 
.07 

$.09 
.08 

$.22 
.05 

$.25 
.12 

$.18 
.11 

$.13 
.10 

$.21 
.06 

$.27 
.05 

$.19 
.07 

$.33 

.08 

$.38 
.05 

$1.12 
.13 

$1.15 

.08 

$1.10 

.18 

$1.14 
.20 

$1.31 
.12 

$1.17 
.11 

$1.15 
.25 

$1.25 
A3 

7. 

$.12 
.05 


What  will  the  following  purchases  cost  ? 


8. 

$.15 
.09 


9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

$.25 

$.12 

$.08 

$.20 

$.38 

$.30 

$.13 

$.24 

.06 

.07 

.13 

.10 

.09 

.18 

.22 

.04 

.11 

.08 

.10 

.06 

.05 

.04 

.07 

.11 

$.50 

$.42 

$.36 

$.54 

$.22 

$.40 

$.62 

$.14 

.08 

.12 

.18 

.09 

.38 

.17 

.25 

.30 

.10 

.03 

.05 

.05 

.10 

.09 

.05 

.03 

$1.20 

$1.00 

$1.25 

$1.50 

$1.10 

$1.05 

$1.40 

$1.60 

.16 

.30 

.50 

.12 

.25 

.15 

.32 

.25 

.06 

.07 

.05 

.10 

.25 

.20 

.08 

.15 

17.   2\  doz.  eggs  @  48<£.  18.   5J  yd.  ribbon  @  40jzf. 

2\  doz.  buttons  @  80^. 


5  lb.  coffee  @  37c7. 
12  lb.  sugar  @  8|c\ 
4  jars  fruit  @  62<£. 

6  lemons  @  2  for  5ff. 
3  doz.  oranges  @  45^. 


3J  yd.  lace  @  75cL 
7  yd.  scrim  @  12^. 
2  yd.  linen  @  62^. 
20  spools  thread  %  60^  a 
dozen. 


88 


UNITED   STATES  MONEY 
Making  Change 


Subtract : 

1.               2. 

3. 

4. 

5. 

6. 

7. 

8. 

$.25         $.25 

$.25 

$.25 

$.25 

$.25 

$.25 

$.25 

.07          .04 

.10 

.16 

.08 

.14 

.06 

.20 





$.25 

$.25 

$.25  ■ 

$.25 

$.25 

$.25 

$.25 

$.25 

.09 

.12 

.15 

.03 

.13 

.17 

.19 

.01 

$.25 

$.25 

$.25 

$.25 

$.25 

$.25 

$.25 

$.25 

.18 

.23 

.21 

.02 

.05 

.11 

.22 

.24 

9. 
$.50 

.38 

10. 

$.50 
.17 

11. 

$.50 
.26 

12. 

$.50 
.11 

13. 

$.50 

.28 

$.50 
.22 

$.50 
.13 

$.50 
.23 

$.50 
.16 

$.50 
^18 

$.50 
.21 

$.50 
.35 

$.50 
.31 

$.50 
.24 

$.50 
.36 

$.75 
.62 

$.75 
.54 

$.75 
.58 

$.75 
.51 

$.75 
.66 

17.  $1.00  —  63^  =  ? 
$1.00  -47*5  -  ? 

$1.00  -  37^  =  ? 
$1.00  -  85^  =  ? 
$1.00  -  19^  =  ? 
$1.00  -  54^  =  ? 
$1.00  -  49^  m  ? 
$1.00  -  72^  =  ? 


18. 


14. 
50 
33 


50 
32_ 

50 
29 


75 
62 


15. 

16. 

.50 

$.50 

.14 

.39 

.50 

.19 


5.50 
.34 

1.75 
.53 


$.50 
.37 

$.50 

.27 

$.75 
.59 


$2.00  - 

$1.55  = 

? 

$2.00  - 

.32  = 

9 

$2.00  - 

.75  = 

? 

$2.00  - 

1.10  = 

? 

$2.00  - 

.88  = 

? 

$2.00  - 

1.20  = 

? 

$2.00  - 

1.85  = 

? 

$2.00  - 

.62  = 

? 

UNITED   STATES  MONEY"  89 

Making  Change 

1.  2.  3.  4. 

500  -  90  500  -  410  500  -  470  500  -  430 . 

500  -  150  500  -  200  500  -  80  500  -  50 

500  -  120  500  -  400  500  -  450  500  -  440 

500  -  60  500  -  250  500  -  300  500  -  70 

500  -  100  500  -  460  500  -  420  500  -  Bi 

$1.00  -  100  $1.00  -  250  $1.00  -  200  $1.00  -  800 

$1.00  -  400  $1.00  -  500  $1.00  -  90  $1.00  -  60 

$1.00  -  70  $1.00  -  700  $1.00  -  600  $1.00  -  300 

Subtract : 

5.      6.  7.      8.  9.      10.  11.     12. 

$1.00       $1.00  $1.00       $1.00  $1.00       $1.00  $1.00       $1.00 

.15           .55  .12           .48  .27          .87  .38          .42 


$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

.68 

.13 

.72 

.36 

.28 

.21 

.43 

.66 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

.45 

.23 

.58 

.61 

.57 

.18 

.65 

.44 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

$1.00 

.78 

.64 

.33 

.26 

.39 

.84 

.62 

.14 

13.   $5.00  -  $2.50  14.   $10.00  -  $3.75  15.    $20.00  -  $15.50 

$5.00  -  $1.75  $10.00  -  $8.10  $20.00  -  $12.00 

$5.00  -  $2.10  $10.00  -  $6.50  $20.00  -  $10.25 

$5.00  -  $3.25  $10.00  -  $.67  $20.00  -  $16.40 

$5.00  -  $4.15  $10.00  -  $9.12  $20.00  -  $8.75 

$5.00  -  $.85  $10.00  -  $4.50  $20.00  -  $9.50 

$5.00  -  $4.45  $10.00  -  $2.25  $20.00  -  $6.15 

$5.00  -  $2.20  $10.00  -  $5.80  $20.00  -  $19.10 

See  Subtraction  of  Decimals  for  further  practice  of  this  kind. 


90  UNITED   STATES  MONEY 

Making  Change 

Use  business  method  in  all  cases. 

•    What  change  should  be  given  back  to  you  at  a  store  if  you  offer 
a  quarter  to  pay  for  articles  which  amount  to 


1. 

15  cents? 

6.   70  and  100? 

11. 

100  and  100? 

2. 

17  cents? 

7.    150  and  30? 

12. 

50  and  70? 

3. 

8  cents? 

8.   40  and  50? 

13. 

120  and  20? 

4. 

6  cents? 

9.    130  and  100? 

14. 

90  and  80? 

5. 

12  cents? 

10.   60  and  100? 

15. 

70  and  80? 

w 

hat  coins  m 

ight 

you  receive  back,  in 

each 

case 

? 

What  change  should  be  given  back  to  you  if  you  offer  a  50-cent 
piece  in  payment  for  articles  which  amount  to 

1.  37i  cents?  6.  250  and  100?  11.  170  and  100? 

2.  15  cents?  7.  200  and  150?  12.  250  and  70? 

3.  25  cents?  8.  160  and  300?  13.  380  and  120? 

4.  40  cents?  9.  120  and  240?  14.  180  and  50? 

5.  12^  cents?  10.  90  and  400?  15.  100  and  330? 

What  coin  or  coins  would  make  the  exact  change? 


What  change  should  you  receive  from  a  clerk  to  whom  you 
hand  a  dollar,  if  your  purchases  amount  to 


1. 

450? 

6. 

500  and  12^0? 

11. 

420  and  180? 

2. 

750? 

7. 

450  and  400? 

12. 

330  and  70? 

3. 

62(5? 

8. 

37J0and5O0? 

13. 

62^0  and  100? 

4. 

87|0? 

9. 

250  and  600? 

14. 

850  and  150? 

5. 

220? 

10. 

190  and  300? 

15. 

200  and  590? 

UNITED   STATES  MONEY 


91 


1.   £  of  $1  is  33£  cents, 
f  of  $1  is  ?    cents. 


Count  by  33^s  to  100.     To  200.     To  300,  and  back  to  33f 
What  is 

2.   Twice  33 J  cents?  3. 

Three  times  33 J  cents? 


Nine  times  33^  cents  ? 


Four  times  33 J  cents? 
Five  times  33 J  cents? 


Seven  times  33 J  cents? 
Eight  times  33 J  cents? 
Ten  times  33  J  cents  ? 
Eleven  times  33 J  cents? 


How  many  articles  @  33^  each  can  be  bought  for 


4.  1  dollar? 
1^  dollars? 
2  dollars? 
6f  dollars? 
10  dollars? 
5 J  dollars? 
12  dollars? 
9  dollars? 


$  7-|? 
$15? 

$  8£? 
$  3f  ? 
$  8? 
$10§? 

$  7? 
$20? 


$10? 
$  1.33  J? 
$  5.66f? 

$18? 
$25?  , 
$20.33  J? 
$  9.66|? 
$30? 


7.   66|^  X  2  =  ? 


mu  X  3  =  ? 


How  many  articles  @  66f  i  each  can  be  bought  for  ! 
For  $12?  For  $6?   For  $20?   For  $8? 
At  66f  i  each,  what  will  be  the  cost  of 

8.   2  articles?  9.   5  articles?  10. 

3  articles?  6  articles? 

4  articles?  7  articles? 


J?  For  $4? 


8  articles  ? 

9  articles? 
10  articles? 


92 


UNITED   STATES  MONEY 


1. 


of  $1  is  16f  cents. 


50^  is  ?  sixths  of  1  dollar. 
16f  ^  is  ?  sixths  of  1  dollar. 
66f  i  is  ?  sixths  of  1  dollar. 
331^  is  ?  sixths  of  1  dollar. 


f  (or  1)  of  1  dollar  is  ?  cents. 
-|  (or  1)  of  1  dollar  is  ?  cents. 
£  (or  § )  of  1  dollar  is  ?  cents, 
f  of  1  dollar  is  ?  cents. 

83-^  is  ?  sixths  of  1  dollar. 

3.  Count  by  16f  's  from  16f  to  100  and  back  to  16 
Count  by  16f  's  to  200  and  back  to  16f . 

4.  Complete  the  table  below  and  memorize  it. 

16f  x  2  = .  16f  x  4  =  - 


16f  X  3  = 


16f  X  6  = 


16|  X  5  m 


How  much  is 

5.   Twice  16f  cents? 
Four  times  16f  cents? 
Six  times  16|  cents? 
Eight  times  16|  cents? 
Ten  times  16f  cents? 


6.   Three  times  16f  cents? 
Five  times  16|  cents? 
Seven  times  16f  cents? 
Nine  times  16f  cents? 
Eighteen  times  16f  cents? 


At  16f  i  each,  how  many  articles  can  be  bought  for 


331  cents? 
66f  cents? 
50  cents? 
83 \  cents? 
100  cents? 

1  dollar? 
\\  dollars? 

2  dollars? 


$11? 
$21? 

$f? 

$4J? 

$1?? 

$10? 

$31? 

$5? 


$1.50? 

$2.66f? 

$3.00? 

$1,331? 

$4.50? 

$  .831? 

$1.66f? 

$1,831? 


10.   What  is  1  of  16f  i  ?     What  part  of  a  dollar  is  this  ? 


UNITED   STATES  MONEY 


93 


|  of  $1  is  12|  cents. 


f  (or  J)  of  $1  is  ?  cents. 

f  of  $1  is  ?  cents. 

|  (or  !)  of  $1  is  ?  cents. 

f  of  $1  is  ?  cents. 

f  (or  f)  of  $1  is  ?  cents. 

J  of  $1  is  ?  cents. 


How  much  is 

3.   Twice  12|  cents? 

Four  times  12!  cents? 

Six  times  12!  cents? 

Eight  times  12!  cents? 

Ten  times  12!  cents? 

Twelve  times  12 \  cents? 


50^  is  ?  eighths  of  1  dollar. 
87!  j£  is  ?  eighths  of  1  dollar. 
25^  is  ?  eighths  of  1  dollar. 
62JC7  is  ?  eighths  of  1  dollar. 
37!  <£  is  ?  eighths  of  1  dollar. 
75^  is  ?  eighths  of  1  dollar. 


4.   Three  times  12 J  cents? 
Five  times  12!  cents? 
Seven  times  12!  cents? 
Nine  times  12 \  cents?   • 
Eleven  times  12!  cents? 
Twenty  times  12!  cents? 


How  many  times  is  12!  c7  contained  in 
5.   25  cents? 

1  dollar? 

\\  dollars? 

50  cents? 

37|  cents? 

1!  dollars? 

62§  cents? 
.  2  dollars? 

75  cents? 

87!  cents? 


Led  in 

$5? 

7.  $  1.50? 

$31? 

$  2.121? 

$4i? 

$10.75? 

$lf? 

$  9.37^? 

$10? 

$  4.25? 

$6J? 

$  7.871? 

$8? 

$    .371? 

$2f? 

$12.50? 

$9? 

$   m\i 

w 

%    .87|? 

94  UNITED   STATES  MONEY 

t.   Count  by  12!'s  from  12|  to  100  and  back  to  12J. 
Count  by  12§'s  to  200  and  back  to  12-|. 

2.   Complete  the  table  below,  and  memorize  it. 

12*  X  2  = .  12J  X  5  -p 

12j  X  3 -m .  12|  x  6  = 

12|  X  4  = .  13}  x  7 

12§  x  8  - . 


How  many  articles  at  12|^  each  can  be  bought  for 

3.   $.87!?  4.    $1.12| ?  5.   $1,624?            6.   $4.12!? 

$.50?  $1.50?  $2.00?  $  5.00? 

$.75?  $1.37!?  $2.50?  $  5.87!? 

$.37!?  $1-75?  $3.00?  $  6.00? 

$.25?  $1.87!?  $3.75?  $  6.25? 

$.62!?  $1.25?  $4.00?  $10.00? 


7.  What  is  !  of  12|{£?     What  part  of  $1  is  this? 

Find  the  cost  of 

8.  2  articles  @  37!j£  each ;    ©  62!^  each ;    @  87!^  each. 

9.  3  articles  @  $1.12!  each;   @  37^  each ;   @  62!^  each. 
10.  4  articles  ®  $1.37|  each ;   @  62-J-fS  each ;   @  87!j4  each. 


UNITED   STATES  MONEY  95 

1.  _i_  of  $1.00  =  ?  -^  of  $1.00  -  ?  2V  of  $1.00  =  ? 

I  of  $1.00  =  ?  iV  of  $1.00  =  ?  TV  of  $1.00  -  ? 

Express  as  a  fractional  part  of  one  dollar : 

2.  $.334  3.   $.50  4.   $.624  5.   $.01 

.12|  .16f  .40  .87i 

.10  .25  .06J  .084 

.05  .37|  .30  .70 

.04  .75  .661  .83* 


press  as  cents  : 

J  of  a  dollar. 

7.     f  of  a  dollar. 

8.   ^5  of  a  dollar. 

4  of  a  dollar. 

f  of  a  dollar. 

^35-  of  a  dollar. 

|  of  a  dollar. 

|  of  a  dollar. 

f  of  a  dollar. 

|  of  a  dollar. 

|  of  a  dollar. 

|  of  a  dollar. 

i  of  a  dollar. 

f  of  a  dollar. 

i^  of  a  dollar. 

■^q  of  a  dollar. 

■^  of  a  dollar. 

i^-  of  a  dollar. 

J  of  a  dollar. 

§  of  a  dollar. 

f  of  a  dollar. 

^  of  a  dollar. 

^  of  a  dollar. 

^  of  a  dollar. 

Read  the  following  amounts  thus :   "$1.40  is  $1| 
9. 


$1.40 

10.   $10.20 

11.   $12.75 

12.   $2.05 

3.87| 

1.334 

9.40 

10.04 

2.10 

15.60 

8.16f 

6.124 

5.50 

2.05 

2.08J 

5.834 

1.121 

3.37-1 

25.121 

7.624 

6.66f 

6.25 

4.064 

15.374 

8.064 

20.75 

16.15 

1.30 

9.80 

4.62| 

5.084 

8.70 

96 


THE  NUMBER  TWENTY-FIVE 


1.   2  X  25  =  ? 

3  X  25  =  ? 

4  X  25  =  ? 

11  X  25 


5  X  25  =  ? 
6X  25  =  ? 
7  X  25  =  ? 


8  X  25  =  ? 

9  x  25  =  ? 
10  x  25  =  ? 


12  x  25  =  ?  . 


2.    Count  by  25's  to  300.     Count  back  to  25. 

Practice  doing  this  until  you  can  do  it  in  20  seconds  or  less. 


3.   How  many  25's  in 

75?            125? 

50? 

25? 

100? 

150? 

200?            175? 

300? 

275? 

250? 

225? 

4.  How  much  money  will  buy  one  thrift  stamp?  Two  thrift 
stamps?  Five?  Eight?  Three?  Twelve?  Four?  Seven? 
Eleven?     Six?     Ten? 


How  many  quarters  in 

• 

$1.?        $4.?        $10.? 

$6.? 

$7.? 

$1.25? 

$1.75? 

$5.?        $3.?        $  8.? 

$9.? 

$2.? 

$2.50? 

$1.50? 

6.  How  much  is 

256  256  and  50^? 

506  25c7,  and  75^? 
25c7,  756  and  25^? 
756  $1.00,  and  25c7? 

7.  What  is  the  sum  of 

25  +  25  +  50  +  25? 
75  +  25  +  25  +  25? 
50+25  +  50  +  25? 
25  +  75  +  50  +  50? 

8.  How  many  times  25%  is 
50%?       100%?       75%?       125%? 

9.  What  is  |  of  25  cents? 
What  is  i  of  25  cents? 


256  $1.00,  and  50c7 
506  756  and  $1.00? 
506  506  and  75^? 
756  756  and  25^? 


50+    25  +  75  +  25? 

100+    50+75  +  25? 

75+  125  +  50  +  50? 

25+  150  +  50  +  25? 

200%?       150%?       175%? 

What  is  |  of  25%? 
What  is  |  of  25%? 


DECIMAL  FRACTIONS     ADDITION 


97 


.2  +  .7  =  ? 

.4  +  .4  =  ? 

•7  +  .2  =  ? 

.5  +  .3  =  ? 

.1  +  .5  =  ? 

.2  +  .6  =  ? 

.3  +  .3  =  ? 

.4  +  .5  =  ? 

Add 


2. 

.3  +  .?  =  ? 

.5  +  .5  =  ? 

.9  +  .4  =  ? 

.8  +  .5  =  ? 

.2  +  .8  =  ? 

.7  +  .3  =  ? 

.4  +  .8  =  ? 

.9  +  .2  =  ? 


3. 

8  +  .6  =  ? 
3  +  .8  =  ? 

9  +  .6  =  ? 

7  +  .5  -  ? 

8  +  .7  =  ? 

6  +  .6  =  ? 

7  +  .7  =  .? 
8+  .8=  ? 


.2  +  .4  +  .3  =  ? 

.1  +  .8  +  .5  =  ? 

3  +  .3  +  .4  =  ? 

.7  +  .5  +  .3  =  ? 

.6  +  .4  +  .9  =  ? 

.8  +  .5  +  .4  =  ? 

.5  +  .7  +  .6  =  ? 

.7  +  .8  +  .5  =  ? 


i: 
5.    .2 

.6 

.5 

.1 

.4 

6. 

.3 

.6 

.3 

.5 

.2 

.6 

.4 

.5 

.5 

.3 

.2 

.3 

.7 

.1 

.6 

.6 

.5 

.6 

.4 

.7 

.4 

.5 

.2 

.2 

.7 

7.    .4 

.6 

.3 

.3 

.4 

8. 

.6 

.4 

.2 

.7 

.6 

.3 

.4 

.7 

.3 

.8 

.1 

.5 

.5 

.3 

.2 

.5 

.5 

£ 

.3 

.2 

.3 

.3 

.5 

.1 

.8 

9.    .4 

.1 

.8 

.7 

.6 

10. 

.8 

.2 

.2 

.4 

.4 

.6 

.3 

.4 

.1 

.3 

.1 

.7 

.8 

.7 

.1 

.2 

.4 

.3 

.9 

.4 

.5 

.4 

.5 

.2 

.1 

5 

.6 

.3 

.1 

.4 

.3 

.1 

.5 

.6 

.8 

11.  3.6  5.8  7.5  2.5  4.3 
.4  .7  .6  .5  .7 
.5      .4      .7       .8      .6 


12.  6.3  1.4  8.6  3.5  7.2 
.6  .4  .2  .3  .9 
.8       .2       .2       .6       .4 


13.  4.1  7.6 
.5  .4 
.3         .5 


3.8 
.5 
.5 


5.5 

.7 
.2 


14.   8.1 

.8 
.6 


4.7 

.7 
.5 


3.6  6.2 
.9  .3 
.1         .7 


15.    1.5      6.8 
5.7      3.3 


4.7 
6.9 


3.8 
5.7 


16.   6.2 
7.9 


5.5 

7.7 


9.5 
3.7 


7.1 
8.3 


98  DECIMAL  FRACTIONS     ADDITION 


1. 

2. 

3. 

4. 

5. 

.4+  .3 

.2  +  .5 

.9  +  .2 

.8 +  .2 

.4 +.7 

.6 +.5 

.3 +  .4 

.7 +  .3 

.3 +  .3 

.8  +  .8 

.5 +  .4 

.9  +  .1 

.6 +  .4 

.7 +  .5 

.6+  .2 

.9 +  .8 

.7 +  .8 

.2 +.7 

.2 +  .2 

.9  +  .0 

.6 +  .7 

.9 +  .7 

.1  +  .0 

.8 +  .3 

.8 +  .4 

.9 +  .3 

.7 +.2 

.5 +  .5 

.5 +  .7 

.9+  .5 

.3  +  .5 

.8  +  .7. 

.4 +.4 

.6 +  .8 

.4  +  .5 

.2 +.9 

.3 +  .9 

.6 +.3 

.7 +  .7 

.3 +  .6 

.3 +  .8 

.5 +  .3 

.8 +  .9 

.     .5 +  .9 

.7 +.9 

.2 +.3 

.7 +  .4 

.4 +  .8 

.2 +  .4 

.3 +  .2 

6. 

7. 

8. 

9. 

10. 

.9 +  .4 

.5 +  .6 

.5 +  .2 

.2 +  .6 

1.4  +  .5 

'  .4  +  .6 

.4 +.9 

.9 +  .6 

1.1  +  .3 

1.0  +  .4 

.3 +  .7 

1.0  +  .2 

1.0  +  .3 

1.5  +  .6 

1.3  +  .7 

.5 +  .8 

.8 +  .6 

.7 +  .6 

1.2  +  .7 

1.1  +  .8 

.6 +  .6 

1,0  +  .7 

.4+  .2 

1.3  +  .2 

1.2  +  .5 

.6 +  .9 

1.2  +  .6 

1.1  +  .7 

1.9 +  .1 

.8 +.2 

.8 +  .5 

1.6  +  .2 

1.2  +  .2 

1.8  +  .5 

1.6  +  .9 

.9 +  .9 

1.9  +  .4 

1.6  +  .6 

1.4  +  .7 

1.0  +  .5 

1.2 +  .1 

1.0  +  .8 

1.5  +  .3 

1.9  +  .3 

1.9  +  .2 

1.7  +  .2 

1.5  +  .7 

1.8 +  .6 

1.6  +  .5 

1.1  +  .5 

11. 

12.   ' 

13. 

14. 

15. 

1.1  +  .9 

1.8  +  .4 

1.3  +  .5 

1.8  +  .8 

1.3  +  .4 

1.6  +  .3 

1.3  +  .3 

1.9  +  .8 

1.4  +  .6 

1.6  +  .7 

1.8  +  .2 

1.3  +  .8 

1.7  +  .8 

1.1  +  .4 

1.0  +  .6 

1.7  +  .6 

1.5  +  .9 

1.2  +  .3 

1.0  +  .9 

1.7  +  .9 

1.2  +  .0 

1.4  +  .2 

1.9  +  .5 

1.7  +  .3 

1.4  +  .3 

1.2  +  .9 

1.7  +  .5 

1.9  +  .9 

1.1  +  .2 

1.6  +  .8 

1.5  +  .8 

1.8  +  .9 

1.6  +  .4 

1.2  +  .8 

1.3  +  .6 

1.8  +  .7 

1.5  +  .5 

1.1  +  .6 

1.7  +  .7 

1.7  +  .4 

1.5  +  .2 

1.2  +  .4 

1.8  +  .3 

1.9  +  .6 

1.9  +  .7 

1.3  +  .9 

1.4  +  .9 

1.4 +  .4 

1.5  +  .4 

1.4  +  .8 

DECIMAL  FRACTIONS     ADDITION  99 


Add: 


1.    .05 

.06 

.04 

.07 

.02 

.05 

.04 

.04 

.05 

.03 

.05 

.03 

.08 

.03 

.06 

.04 

2.    .06 

.03 

.05 

.04 

.08 

.07 

.09 

.08 

.07 

.08 

.09 

.07 

.08 

.07 

.04 

J05 

3.    .16 

.21 

.15 

.19 

.25 

.32 

.44 

.32 

.07 

.04 

.08 

.04 

.06 

.08 

.06 

.08 

4.   .38 

.06 

.35 
.05 

.61 
.08 

.28 
.05 

.33 

.08 

.57 
.04 

.68 
.05 

5.04 

.18 

.72 
.08 

5.    1.05 
.13 

2.17 
.06 

4.25 
.12 

3.34 

.08 

6.08 
.15 

7.18 
.07 

2.27 
.11 

10. 


11. 


6.  5.14  8.91  6.16  5.28  3.18  5.22  1.19  4.35 

.02  .08  .08  .07  .09  .08  .15  .07 

7.  1.02  5.24  3.05  4.10  8.11  2.20  5.05  3.25 
6.14  1.33  2.20  6.35  1.80  3.17  1.60  2.20 

8.  5.04  3.19  2.15  6.18  4.16  1.25  2.14  1.13 
1.67  1.21  6.15  2.18  4.16  1.25  7.08  2.09 


.75 

.24 

.55 

.37 

.87 

.15 

.45 

.58 

.68 

.89 

.66 

.25 

.34 

.98 

.79 

.37 

.02 

.25 

.13 

4.18 

6.22 

.37 

.19 

.54 

.16 

2.51 

3.12 

.22 

.15 

5.52 

2.11 

.05 

2.42 

.18 

.66 

.05 

.25 

.03 

.07 

1.23 

.05 

.03 

.02 

3.11 

.12 

.42 

2.05 

5.22 

1.20 

.54 

.25 

.05 

4.23 

1.12 

.11 

.33 

.10 

1.02 

2.62 

.22 

.04 

.03 

.52 

.01 

100  DECIMAL  FRACTIONS     SUBTRACTION 

1.    .9  -  .4  2.    .07  -  .03  3.    1.7  -  .5           4.   5.9  -  ,6 

.8  -  .3  .09  -  .06  1.8  -  .7  3.7  -  .3 

.7  -  .2  .08  -  .05  2.4  -  .3  2.6  -  .5 

.6  -  .1  .05  -  .01  3.6  -  .6  4.8  -  .3 

.9  -  .6  .06  -  .03  4.8  -  .5  3.9  -  .5 

.8  -  .4  .09  -  .07  1.9  -  .8  2.5  -  .4 

.7  -  .3  .08  -  .03  2.7  -  .4  3.7  -  .2 

.5  -  .2  .07  -  .02  5.B  -  .6  5.6  -  .4 

.9 -.5  .09 -.04  1.5 -.5  4.4  -  .4 

.8  -  .2  .08  -  .07  3.9  -  .4  2.8  -  .7 


Subtract : 

5.  1.7  1.8  2.4  3.6  4.8  1.9  2.7  5.8 

.5  .1  .3  .6  .5  .4  .3  .6 

6.  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0 

.7  .5  .2  .3  .8  .9  .6  .4 

7.  2.0  5.0  3.0  6.0  9.0  4.0  7.0  8.0 

.3  .7  .8  .2  .4  .9  .5  .6 

8.  1.5  2.4  3.7  5.4  7.3  2.2  3.3  6.3 

.8  .6  .8  _A  _A  _A  __£  JL 

9. 


.9 

.8 

.6 

.5 

.7 

.4 

.3 

.8 

.05 

.02 

.08 

.04 

.06 

.07 

M 
.5 

.09 

.7 

.9 

.4 

.6 

.4 

.8 

.7 

.12 

.54 

.22 

.35 

.11 

.33 

.27 

.46 

10. 


11.  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00 

.22  .36  .53  .61  .47  .28  .89  .74 

12.  .45  .64  .33  .41  .55  .84  .77  .62 
^  .18  45  .12  .36  .29  .18  .27 

13.  1.09  3.25  2.16  1.17  5.22  3.06  4.32  9.11 

.35  .16  .52  .48  .15  .25  .25  .04 


DECIMAL  FRACTIONS 

^JJB^rRACTION  \  \ 

101 

Subtract : 

1. 

.4 

.8 

.9 

1.2 

1.3 

2. 

1.9 

1.3 

.9 

.7 

1.8 

.2 

.4 

.9 

.8 

.4 

.2 

1.0 

.6 

.4 

.9 

3. 

1.5 

1.8 

1.4 

2.0 

.8 

4. 

1.5 

1.9 

1.4 

1.3 

.8 

1.3 

1.0 

.5 

.6 

.7 

.8 

.9 

1.0 

.5 

,3 

5. 

1.0 

1.1 

1.8 

1.9 

.5 

6. 

1.6 

1.1 

1.7 

1.1 

1.6 

.2 

.7 

1.3 

L6 

.5 

.9 

1.0 

.9 

.8 

1.3 

7. 

2.0 

1.9 

.5 

1.2 

1.5 

8. 

2.0 

1.0 

1.7 

2.0 

.5 

1.5 

1.2 

.2 

.4 

_7 

.7 

.9 

1.1 

.2 

.3 

9. 

1.7 

1.8 

1.3 

.9 

1.7 

10. 

1.2 

1.7 

1.6 

2.0 

1.2 

1.2 

1.5 

.6 

.5 

_£ 

.6 

1.4 

1.0 

.4 

.9 

11. 

.6 

1.0 

1.6 

1.9 

.3 

12. 

.5 

1.1 

1.7 

1.3 

.9 

.3 

.6 

1.5 

.7 

.3 

.4 

.5 

1.0 

.7 

.3 

13. 

.3 

1.1 

1.9 

1.4 

2.0 

14. 

1.3 

1.9 

1.6 

.6 

2.0 

.2 

.6 

.5 

1.1 

.0 

.8 

1.4 

.8 

.2 

1.3 

15, 

1.4 

.7 

1.9 

1.3 

1.5 

16. 

1.7 

.8 

1.0 

.8 

.7 

.6 

.2 

.3 

1.1 

1.4 

1.3 

& 

.5 

.2 

.6 

17. 

1.3 

1.6 

1.8 

2.0 

1.0 

18. 

1.2 

.6 

1.5 

.9 

1.6 

1.2 

1.1 

1.4 

1.6 

.7 

1.1 

.5 

.9 

J5 

.7 

19. 

.9 

1.5 

1.9 

2.0 

1.1 

20. 

.7 

1.4 

1.8 

1.9 

1.2 

.2 

.6 

1.1 

1.4 

.3 

J 

.8 

1.1 

1.3 

.7 

21. 

.9 

1.2 

2.0 

1.6 

.2 

22. 

1.2 

1.4 

1.3 

2.0 

1.5 

.4 

.5 

.5 

1.2 

.2 

.3 

.7 

.9 

1.2 

1.2 

23. 

.7 

2.0 

1.9 

1.1 

.9 

24. 

.6 

1.1 

2.0 

1.8 

2.0 

.5 

.3 

.4 

.2* 

.7 

.4 

.9 

.8 

1.6 

1.9 

25. 

1.8 

.8 

.8 

.7 

1.4 

26. 

10. 

1.0 

1.7 

2.0 

1.5 

1.2 

.6 

.5 

.3 

1.3 

.8 

4 

1.6 

.9 

1.0 

102  :  ^;(^MAL  FRACTIONS     SUBTRACTION 


1.   .14  -  .09 

2.    .75  -  .07 

3.    .61  -  .02 

4.   .16  -  .06 

.24  -  .07 

.59  -  .06 

.20-  .09 

.50  -  .08 

.90  -  .03 

.22  -  .05 

.99  -  .04 

.83  -  .06 

.65  -  .06 

.67  -  .03 

.86  -  .05 

.44  -  .04 

.82  -  .04 

.52  -  .08 

.39  -  .09 

.60  -  .05 

5.    .29  -  .07 

6.    .24  -  .09 

7.    .58  -  .09 

8.    .34  -  .03 

.73  -  .03 

.71  -  .04 

.40  -  .07 

.42  -  .07 

.35  -  .06 

.96  -  .08 

.26  -  .03 

.68  -  .02 

.89  -  .05 

.64  -  .02 

.33  -  .02 

.23  -  .08 

.55  -  .08 

.19  -  .05 

.12  -  .04 

.92  -  .07 

9.    .80  -  .06 

10.    .97  -  .06 

11.    .30  -  .02 

12.    .27  -  .03 

.37  -  .05 

.45  -  .05 

.17  -  .08 

.98  -  .06 

.69  -  .02 

.31  -  .09 

.65  -  .04 

.36  -  .07 

.56  -  .04 

.72  -  .05 

.57  -  .07 

.41  -  .05 

.18  -  .07 

.66  -  .08 

.95  -  .09 

.63  -  .04 

13.    .72  -  .02 

14.    .15  -  .02 

15.    .81  -  .03 

16.    .11  -  .07 

.13  -  .07 

.32  -  .05 

.48  -  .08 

.38  -  .05 

.87  -  .09 

.94  -  .08 

.70  -  .07 

.74  -  .02 

.76  -  .04 

.78  -  .03 

.93  -  .09 

.21  -  .06 

.88  -  .07 

.25  -  .06 

.54  -  .03 

.43  -  .07 

17.    .84  -  .05 

18.    .49  -  .08 

19.    .47  -  .04 

20.    .20  -  .03 

.46  -  .07 

.53  -  .04 

.33  -  .05 

.83  -  .04 

.91  -  .08 

.77  -  .02 

.64  -  .03 

.74  -  .06 

.79  -  .03 

.51  -  .05 

.95  -  .06 

.36  -  .02 

.28  -  .04 

.85  -  .03 

.56  -  .09 

.71  -  .05 

21.    .92  -  .09 

22.    .17  -  .08 

23.    .78  -  .05 

24.    .54  -  .06 

.63  -  .02 

.96  -  .04 

.44  -  .09 

.93  -  .09 

.40  -  .04 

.52  -  .03 

.55  -  .03 

.18  -  .05 

.35  -  .05 

.80  -  .06 

.39  -  .04 

.31  -  .07 

.68  -  .07 

.15  -  .07 

.41  -  .05 

.62  -  .08 

DECIMAL  FRACTIONS     MULTIPLICATION  103 


1. 

2. 

3. 

4. 

5. 

2X  .2 

3X.3 

4X  .8 

5x.2 

6X.7 

2X.5 

3X  .8 

4X  .4 

5x.9 

6X.3 

2X  .4 

3X.4 

4X.2 

5x  .6 

6x  .8 

2X.9 

3X.9 

4x  .6 

5x  .8 

6X.9 

2X.3 

3X.5 

4x  .7 

5x  .5 

6x  .2 

2X.6 

3X  .2 

4X.5 

5x  .3 

6x  .5 

2X  .8 

3X  .6 

4x  .9 

5x  .7 

6x  .6 

2X.7 

3X.7 

4X.3 

5X.4 

6X.4 

6. 

7. 

8. 

9. 

10. 

7x  .08 

8X  .03 

9  x  .05 

10  x  .06 

12  X  .09 

7x  .02 

8X  .05 

9x  .02 

10  x  .02 

12  x  .02 

7x  .03 

8X  .09 

9x  .08 

10  X  .03 

12  x  .08 

7x  .06 

8X  .02 

9x  .06 

10  X  .05 

12  x  .06 

7x  .09 

8X  .06 

9x  .03 

11  X  .09 

12  X  .03 

7x  .04 

8X  .04 

9x  .07 

11  X  .07 

12  X  .07 

7x  .07 

8x  .07 

9x  .-04 

11  X  .04 

12  x  .04 

7X.05 

8x  .08 

9x  .09 

11  X  .08 

12  x  .05 

Multiply : 

11.   .9 

.2        .4 

.6         .7 

3         .4         .9 

.2         .8 

.2 

.6        .9 

.5         .3 

6         .7         .6 

.3         .2 

12. 

.5 

.7 

.4 

.6 

.7 

.6 

.4 

.3 

.5 

.7 

.5 

.9 

.4 

& 

.5 

.6 

.5 

.7 

.8 

.7 

13. 

.05 

.12 

.04 

.06 

.11 

.15 

.03 

.09 

.01 

.14 

.5 

.5 

.4 

.3 

.7 

.6 

.9 

_JS 

.9 

.2 

14. 

1.2 

1.1 

8.4 

7.5 

2.1 

1.5 

7.0 

4.2 

1.3 

1.8 

• 

_7 

.9 

.2 

.4 

_£ 

.6 

.5 

.3 

.7 

.2 

15. 

.06 

.12 

.15 

.22 

.07 

.25 

.11 

.33 

.16 

.01 

.04 

.08 

.05 

.02 

M 

.03 

.12 

.03 

.05 

.01 

104  DECIMAL  FRACTIONS     MULTIPLICATION 


1. 

6X.7 

2. 

2X.3 

3. 

2X.2 

4. 

9X  .3 

3X.5 

3X  .9 

4x  .9 

6X.4 

11  X  .7 

11  X. 3 

7x  .7 

7x  .8 

5X.9 

4X.2 

8X  .5 

9X.7 

2X.4 

5X.7 

7X.3 

10  X  .8 

5. 

3x  .2 

6. 

11  X  .8 

7. 

8X.6 

8. 

8X  .4 

8X.8 

6x  .6 

7X.9 

12  X  .3 

4X.6 

5x  .4 

12  X. 5 

10  X. 2 

6X.7 

12  X  .2 

8X.7 

12  x  .4 

10  x. 5 

2X.9 

11  X. 9 

9X.5 

9. 

9X.4 

10. 

5X.6 

il- 

2x.6 

12. 

9x  .6 

11  X  .5 

3X.7 

4x  .8 

3X  .8 

10  X. 3 

6X.3 

10  x  .7 

4x  .5 

6x  .2 

11  X. 2 

8X.3 

6x  .8 

9X.8 

7x  .4 

5X.2 

12  X. 7 

13. 

11  X  .6 

14. 

10  X  .9 

ls. 

6x.9 

16. 

4X.3 

3X.4 

7X.6 

2x  .8 

4x7 

8X.2 

5X.3 

5X.5 

10  X. 4 

9X.9 

2X.7 

10  X  .6 

7X  .5 

6X.5 

12  X  .6 

9x.7 

3X.6 

17. 

7X.2 

18. 

11  X  .4 

19. 

7x  1.0 

20. 

8x  1.0 

4X.4 

3X.3 

3x  1.1 

2x  1.2 

7x.8 

9x  .2 

5x  1.2 

7x1.1 

2X.5 

5X.8 

3x  1.0 

4x  1.0 

8X.9 

2x  1.0 

2x1.1 

3X  1.2 

21. 

4x1.1 

22. 

5x  1.1 

23. 

6X  1.0 

24. 

7x  1.2 

9X  1.0 

6x  1.2 

8X  1.1 

10  X  1.1 

6x  1.1 

11  X  1.0 

12  X  1.2 

12  X  1.1 

4x  1.2 

9x  1.1 

11  X  1.0 

8x  1.2 

5x  1.0 

12  X  1.0 

9x  1.2 

10  X  1.2 

7x1.1 

11  X  1.2 

10  X  1.0 

11  X  1.1 

DECIMAL  FRACTIONS     MULTIPLICATION  105 

Multiply : 


1. 

.09 

04 

05 

.03 

02 

08 

.12 

.11 

2 

9 

11 

10 

6 

9 

4 

3 

2. 

.06 

.07 

.12 

.03 

.02 

04 

.09 

.02 

5 

3 

8 

6 

11 

7 

6 

__3 

3. 

.11 

.08 

.05 

.06 

.07 

.03 

.08 

.11 

8 

2 

5 

10 

9 

2 

12 

_6 

4. 

.04 

.06 

.07 

.12 

.02 

.04 

.06 

.08 

4 

8 

5 

6 

12 

5 

6 

11 

5. 

.12 

.03 

.05 

.07 

.09 

.11 

.12 

.02 

11 

7 

8 

7 

4 

2 

12 

_7 

6. 

.11 

.03 

.04 

.09 

.05 

.08 

.06 

.07 

9 

3 

11 

8 

2 

7 

12 

2 

7. 

.12 

.07 

.11 

.03 

.06 

.09 

.04 

.07 

2 

6 

4 

5 

7 

5 

2 

11 

8. 

.12 

.09 

.11 

.02 

.03 

.07 

.08 

.06 

3 

10 

5 

5 

_8 

10 

4 

2 

9. 

.04 

.05 

.09 

.02 

.03 

.11 

.04 

.12 

12 

9 

12 

10 

12 

7 

8 

5 

10. 

.05 

.07 

.06 

.08 

.12 

.02 

.11 

.03 

10 

6 

4 

8 

7 

9 

11 

9 

11. 

.09 

.08 

.04 

.05 

.02 

.09 

.03 

.05 

7 

10 

6 

3 

4 

3 

11 

7 

12. 

.08 

.06 

.04 

.07 

.11 

.12 

.03 

.05 

5 

3 

10 

4 

10 

9 

4 

6 

13. 

.11 

.09 

.02 

.04 

.06 

.07 

.08 

.12 

12 

9 

8 

3 

11 

12 

6 

10 

106 


DECIMAL  FRACTIONS     DIVISION 


1. 
.6*  .3 

1.2  +  .6 

2.0  4-  .5 
1.5  -  .3 

2.4  +  .6 

3.2  -r-  .4 

2.1  -  .7 

2.5  -  .5 

3.3  -  .3 
3.0  +  .5 


2. 
1.2-  .2 
1.6  4-  .4 
1.8  -  .9 
2.1  -  .3 

1.6  4-  .8 

2.7  -  .9 
3.5  +  .7 
1.0  -  .2 

1.8  ^  .6 
3.0  -  .3 


.9 
1.4 


3. 

*  .2 
.3 
.2 


1.0  -  .5 


2.0- 
1.5 


2.7  -^  .3 

2.8  -  .7 


3.0 
3.6 


.6 
.3 


1.8  -  .2 
2.4  -  .4 
1.2 
2.2  -  .2 

2.8  -v-  .4 


3.5 

2.0 

2.4- 

3.6 

2.4 


.5 
.2 
.8 
.9 
.3 


5. 

.8-  .4 
3.2 
1.4  -  .7 


1.6 
2.4 


3.6 


.2 
1.2 


3.0-  1.0 
2.2  -  1.1 


1.2 


2.0  -  1.0 
3.3  -r-  1.1 


Divide : 

6. 

8)4.0 

7. 

12)4.8 

8. 
5)4.0 

9. 

.6)36 

10. 

.4)80 

11. 
1.1)55 

7)5.6 

11)7.7 

9)4.5 

.5)45 

.6)60 

1.2)108 

5)6.0 

10)7.0 

2)6.6 

.6)66 

.8)96 

1.5)30 

8)4.8 

21)4.2 

8)8.0 

.8)56 

.4)100 

2.5)100 

5)7.5 

25)5.0 

6)7.2 

.7)70 

.2)40 

1.5)75 

7)4.2 

12)6.0 

5)5.5 

.6)48 

.3)66 

1.6)32 

9)5.4 

25)7.5 

7)4.9 

.4)44 

.2)32 

2.1)42 

7)8.4 

40)8.0 

4)4.0 

.6)42 

3)45 

3.3)99 

12. 
.7  ^-. 5 
.9 -.2 
.5  4-  .4 

.8  4-  .3 
.6  4-  .5 


13. 

2.3- 
3.2- 
1.9- 
4.5- 

2.5  -=-  .8 


.4 
.5 

.6 

.7 


14. 

2.8  -  .9 
3.7 
4.8 
5.5  +  .6 


1.4 


.3 


15. 

3.5-  1.1 
4.9  4-  1.2 
5.2  -  2.5 

3.4  -  1.5 

2.5  4-  1.2 


16. 
4.5  -  2.2 
6.8  -  1.1 
3.8  -  1.2 
1.7  -  1.4 
6.3  -f-  1.5 


DECIMAL  FRACTIONS     DIVISION 


107 


1. 


$.08 


.18-5-  .02 
.12 -h  .02 
.06  *    .03 


.08 


.16 


.32 


$.04 


.02 


.09 -f-    .03 
.12-    .06 


.04 


24-    .04 


.08 


;.12 

.18 
.14 
.15 
.21 
.24 
.22 
.27 
.35 
.18 


$.03 
.09 
.02 
.03 
.03 
.06 
.02 
.09 
.07 
.06 


3 
.14  - 

.25- 
.32- 
.21  - 
.33  - 
.15- 
.27- 
.28- 
.36- 
.35- 


$.07 
.05 
.04 
.07 
.03 
.05 
.03 
.07 
.03 
*■    .05 


.36 

.16 
.24 
.22 
.16 
.18 
.12 
.24 
.28 
.36 


$.09 
.02 
.12 
.11 
.08 
.02 
.04 
.08 
.04 
.06 


Divide : 
5. 

6. 

7. 

8. 

9. 

10. 

7).42 

.04)36. 

.7).84 

.oi)a 

1.2)1.44 

.13)3.9 

82,56 

.08)72. 

.6)^66 

.032,9 

2.5)1.50 

.04)4.4 

7)  .63 

.03)21. 

.9).81 

.02)^8 

1.2)  .96 

.09)7^2 

5).60 

.09)54. 

.7^28 

.03)^6 

1.1)1.32 

.15)7.5 

1)  .56 

.06)48. 

.9)  .27 

.05^5 

1.5).75 

.03)8.1 

9)^99 

.12)72. 

.7).35 

.01^3 

1.2).84 

.12)9.6 

6).54 

.07)49. 

.8). 64 

.04^8 

1.1)1.10 

.07)7.0 

8)  .24 

.04)32. 

.9). 63 

m)A 

1.7)1.70 

.02)2.6 

11. 

,.25)$6.00 


12. 
.07)$5.11 


.18)  3.60  .12)  1.80 

.07)  1.54  .09)  2.79 

.35)  7.00  .08)  6.02 

.02)  1.50  .11)  3.52 


13. 

i.09)$189. 


.08)  256. 
.11)  451. 
.05)  100. 


14. 

6)$8.40 


.07)  140.  4)  7.20 


3)  1.26 
5)  2.00 
9)  6.03 


15. 

S.04)$18.4 

.02)  66.6 

.08)  17.6 

.07)  23.1 

.12)  37.2 


.08 

DECIMAL  FRACTIONS     DIVISION 

l 

2 

• 

3. 

4. 

1.6- 

•-  A 

6.6- 

-  .6 

6.0- 

-  .6 

2.2- 

-  .2 

4.8- 

-  .6 

9.6- 

'-  .8 

8.8- 

=-  1.1 

1.8- 

-  .3 

3.5- 

-  .7 

6.3- 

-  .7 

.6- 

-  .2 

9.6- 

-  1.2 

1.2- 

-  .2 

2.5- 

-  .5 

5.4- 

-  .9 

2.1  - 

-  .7 

.6- 

-  .3 

1.6- 

-  .8 

2.8- 

-  .4 

3.0- 

-  .6 

5 

6. 

7. 

8. 

3.3- 

-  1.1 

3.6- 

-  .4 

3.6- 

-  .6 

3.6- 

-  .9 

4.8- 

-  1.2 

5.0- 

-1.0 

8.8- 

-  .8 

2.2  - 

-  1.1 

2.1  - 

-  .3 

1.8- 

-  .9 

2.0- 

-  1.0 

1.4- 

-  .2 

3.0- 

-  .3 

2.4- 

-  .2 

4.0- 

-  .5 

.9- 

-  .3 

5.5- 

-  .5 

2.0- 

-  .4 

4.9- 

-  .7 

4.0- 

-  1.0 

9 

1C 

l. 

11. 

12 

$.24- 

-  $.03 

$.45- 

-  fo.05 

$.60- 

-$.12 

$.84- 

-$.12 

.70- 

-    .07 

.20- 

-    .02 

.50- 

-    .05 

.18- 

-    .02 

.32- 

-    .08 

.30- 

-    .10 

.42- 

-    .07 

.80- 

-    .10 

.12- 

-    .06 

.36- 

-    .03 

.24- 

-    .06 

.27- 

-    .03 

.48- 

-    .04 

.32- 

-    .04 

.64- 

-    .08 

.63- 

-    .09 

13 

14 

15. 

16 

$.80- 

-  $.08 

$.33  - 

-$.03 

$.40- 

-  $.04 

$.16- 

-  $.02 

.24- 

-    .04 

.90- 

-    .10 

.28- 

-    .07 

.12- 

-    .04 

.15- 

-    .05 

.40- 

-    .08 

.12- 

-    .03 

.66- 

-    .06 

.08- 

-    .02 

.18- 

-    .06 

.30- 

-    .05 

.84- 

-    .07 

.27- 

-    .09 

.35- 

-    .05 

.81  - 

-    .09 

.48- 

-    .08 

11 

? 

U 

I. 

19. 

2C 

>. 

;  .20- 

-  $.05 

$  .24- 

-  $.08 

$  .54- 

-  $.06 

$  .56- 

-  $.07 

.99- 

-    .09 

.60- 

-    .05 

.63- 

-    .07 

.42- 

-    .07 

.56- 

-    .08 

.72- 

-    .12 

1.10- 

-    .11 

1.32- 

-    .12 

1.08- 

-    .12 

1.20- 

-    .12 

1.20- 

-    .12 

.77- 

-    .11 

1.21  - 

h    .11 

1.44- 

i-    .12 

.72- 

-    .12 

1.00- 

-    .10 

DENOMINATE  NUMBERS  109 

What  name  is  given  to 

1.   J  of  a  yard?  2.    12  times  a  unit? 

|  of  a  quart?  100  times  a  cent? 

J  of  a  pint  ?  24  times  an  hour  ? 

iV  of  a  dollar  ?  20  times  a  unit  ? 

4-  of  a  week  ?  36  times  an  inch  ? 

i  of  a  bushel  ?  60  times  a  minute  ? 

•^  of  a  year  ?  9  times  a  square  foot  ? 

^  of  a  pound  ?  2000  times  a  pound  ? 

|  of  a  peck?  100  times  a  year? 

\  of  a  gallon?  320  times  a  rod? 

TX2-  of  a  foot  ?  32  times  a  quart  ? 

8  times  a  pint? 


Give  answers  to  the  following  questions  in  their  lowest  terms : 

3.  4  quarts  is  what  fractional  part  of  a  bushel? 
8  units  is  what  fractional  part  of  a  dozen? 
10  months  is  what  fractional  part  of  a  year  ? 
12  ounces  is  what  fractional  part  of  a  pound? 
24  minutes  is  what  fractional  part  of  an  hour? 

4.  4|  inches  is  what  fractional  part  of  a  yard? 
200  pounds  is  what  fractional  part  of  a  ton? 
3  days  is  what  fractional  part  of  a  week? 

2  pints  is  what  fractional  part  of  a  gallon? 
16  hours  is  what  fractional  part  of  a  day? 


Express 

5.  2  quarts  and  1  pint  as  the  fraction  of  a  gallon. 
2  feet  and  9  inches  as  the  fraction  of  a  yard. 

1  peck  and  4  quarts  as  the  fraction  of  a  bushel. 

6.  3  gallons,  3  quarts,  and  1  pint  as  gallons. 

10  bushels,  3  pecks,  and  4  quarts  as  bushels. 
5  yards,  2  feet,  and  9  inches  as  yards. 


110 


DENOMINATE  NUMBERS 


3  hr.  is  how  many  min.  ? 

2  lb.  is  how  many  oz.? 

4  gal.  is  how  many  qt.  ? 

4  ft.  is  how  many  in.  ? 

3  wk.  is  how  many  da.? 

5  yr.  is  how  many  mo.  ? 

4  bu.  is  how  many  pk.  ? 
10  min.  is  how  many  sec? 


2. 

6  sq.  yd.  is  how  many  sq.  ft.? 

8  pk.  is  how  many  qt.  ? 
12  yd.  is  how  many  ft.  ? 

9  dol.  is  how  many  qr.  ? 

5  doz.  is  how  many  units? 
2  rd.  is  how  many  ft.  ? 
16  qt.  is  how  many  pt.? 
2  da.  is  how  many  hr.? 


Express 

3£  bushels  as  pecks. 

4^  feet  as  inches. 

2.5  days  as  hours. 

2\  (short)  tons  as  pounds. 

1^  feet  as  inches. 

5J  dozen  as  units. 
.    1.5  bushels  as  pecks. 

\  yard  as  inches. 


Express 
f  of  a  yard  as  inches. 
\\  yards  as  inches. 
4  rods  as  feet. 
1\  years  as  months.   , 
\\  dollars  as  cents. 
8£  pecks  as  quarts. 
2\  quires  as  sheets. 
3$  sq.  yards  as  sq.  feet. 


5. 

How  many  hr.  in  5  da.  ? 
How  many  sec.  in  1  hr.  ? 
How  many  pt.  in  4  gal.  ? 
How  many  gal.  in  60  pt.  ? 
How  many  qt.  in  If  bu.  ? 
How  many  bu.  in  176  qt.  ? 
How  many  yr.  in  180  mo.  ? 
How  many  hr.  in  If  da.? 


6. 


How  many  sq.  rd.  in  f  A.  ? 
How  many  rd.  in  2  mi.? 
How  many  in.  in  2\  yd.  ? 
How  many  ft.  in  \  mi.  ? 
How  many  gi.  in  2  gal.  ? 
How  many  pt.  in  2\  pk.  ? 
How  many  oz.  in  5£  lb.? 
How  many  rt.  angles  in  270° 


DENOMINATE  NUMBERS 


111 


1. 


How  many  qt.  in  16  pt.? 
How  many  wk.  in  84  da.  ? 
How  many  lb.  in  48  oz.  ? 
How  many  gal.  in  40  qt.  ? 
How  many  yd.  in  72  in.  ? 
How  many  da.  in  48  hr.  ? 
How  many  doz.  in  96  units? 
How  many  yd.  in  36  ft.  ? 


si. 

How  many  hr.  in  600  min.  ? 
How  many  bu.  in  24  pk.  ? 
How  many  pk.  in  56  qt.? 
How  many  min.  in  120  sec? 
How  many  ft.  in  84  in.  ? 
How  many  rd.  in  11  yd.? 
How  many  sq.  yd.  in  27  sq.  ft.  ? 
How  many  yr.  in  120  mo.  ? 


3. 

75  qt.  is  how  many  gal.  ? 
30  in.  is  how  many  ft.  ? 
15  pt.  is  how  many  qt.  ? 
66  mo.  is  how  many  yr.  ? 
20  oz.  is  how  many  lb.  ? 
25  ft.  is  how  many  yd.  ? 
30  units  is  how  many  doz.? 
100  min.  is  how  many  hr.  ? 


4. 
22  pk.  is  how  many  bu.? 
20  qt.  is  how  many  pk.  ? 
15  da.  is  how  many  wk.? 
72  sq.  in.  is  how  many  sq.  ft.? 
60  sheets  is  how  many  quires? 
5280  ft.  is  how  many  miles  ? 
5000  1b.  is  how  many  T.? 
45  in.  is  how  many  yd.  ? 


Express 

4  rods  as  yards. 
£  mile  as  rods. 
1^  rt.  angles  as  degrees. 
36  sq.  inches  as  sq.  feet. 
2  cu.  yards  as  cu.  feet. 
2  cords  as  cubic  feet. 
\  cord  as  cubic  feet. 
1  ream  as  sheets. 


6. 

Express 
20  tons  as  pounds. 
\\  square  feet  as  square  inches. 
100  quarts  as  bushels. 
\  bushel  as  pints. 
75  units  as  dozens. 
88  days  as  weeks. 
2318  cents  as  dollars. 
345  minutes  as  hours. 


112 


DENOMINATE  NUMBERS 


1. 

Express 

1  ft.  4  in.  as  inches. 

2  yd.  1  ft.  as  feet. 

3  gal.  2  qt.  as  quarts. 
1  lb.  6  oz.  as  ounces. 

4  pt.  2  gi.  as  gills. 

3  score  and  10  yr.  as  years. 

3  bu.  3  pk.  as  pecks. 

4  pk.  7  qt/as  quarts. 


2. 
Express 

31  qt.  as  gallons. 
40  oz.  as  pounds. 
17  ft.  as  yards. 
50  in.  as  feet. 
63  da.  as  weeks. 
30  hr.  as  days. 
75  mo.  as  years. 
100  units  as  dozens. 


3. 

Express 

4  T.  8  cwt.  as  cwt. 
3  da.  6  hr.  as  hours. 

5  yr.  8  mo.  as  months. 

5  hr.  30  min.  as  minutes. 
2  mi.  18  rd.  as  rods. 
10  min.  10  sec.  as  seconds. 
8  lb.  2  oz.  as  ounces. 
12  bu.  3  pk.  as  pecks. 


Express 
4500  lb.  as  tons. 
250  min.  as  hours. 
117  qt.  as  gallons. 
200  sq.  rd.  as  acres. 
150  in.  as  feet, 
f  A.  as  sq.  rods, 
f  da.  as  hours, 
f  lb.  as  ounces. 


Express 

13  gal.  1  qt.  1  pt.  as  quarts. 
2  T.  5  cwt.  5  lb.  as  pounds. 
2  rd.  2  yd.  2  ft.  as  feet. 

2  rd.  12  ft.  6  in.  as  feet. 

1  bu.  3  pk.  4  qt.  as  quarts. 

3  da.  8  hr.  10  min.  as  hours. 
15°  _  45'  _  30"  as  minutes. 


RECKONING  TIME  113 

Pupils  in  elementary  grades  should  go  through  these  exercises 
first  with  the  aid  of  the  clock  face,  clearly  visualizing  each  thought 
process. 

How  long  a  time  is  it 

1.   From  9  a.m.  to  7  p.m.?  2.   From  7.30  p.m.  to  6.30  a.m. ? 
From  8  a.m.  to  5.30  p.m.?  From  11.30  p.m.  to  9  a.m.? 

From  7  a.m.  to  6  p.m.?  From  7.45  p.m.  to  6  a.m.? 

From  8.30  a.m.  to  4  p.m.?  From  10  p.m.  to  7.30  a.m.? 

From  10.30  a.m.  to  8  p.m.  ?  From  9.30  p.m.  to  7  a.m.  ? 

At  what  time  must  you  start  in  order  to  reach  your  destination 
at  7.45  a.m.  if  the  walk  requires 

3.   20  minutes?  4.     5  minutes?  5.    10  minutes? 

Half  an  hour  ?  25  minutes  ?  35  minutes  ? 

15  minutes?  8  minutes?  3  minutes? 

6.  If  your  watch  is  8  minutes  fast,  what  time  is  it  when  your 
watch  says  4.15?     12.30?    3.45?    6.18?    Noon?    8.04? 

How  many  minutes  of  each  school  day  should  be  given  to  a  daily 
subject  which  is  scheduled  to  have 

7.  2|  hours  per  week?  8.    4  hours  per  week? 
If  hours  per  week?  1J  hours  per  week? 
6  hours  per  week?                                      3 J  hours  per  week? 

Find  the  time  that  a  train  may  be  expected  to  arrive,  if 

9.  10. 

Due  at  11.20 ;  40  minutes  late.  Due  at  9.10 ;  1  hr.  20  min.  late. 

Due  at  6.45  ;  35  minutes  late.  Due  at  4.35 ;  45  minutes  late. 

Due  at  10.12 ;  18  minutes  late.  Due  at  8.54 ;  10  minutes  late. 

Due  at  3.22 ;  50  minutes  late.  Due  at  7.37 ;  25  minutes  late. 

Due  at  5.48 ;  30  minutes  late.  Due  at  1.15 ;  55  minutes  late. 


114 


PERCENTAGE 


What  per  cent  of  a  number  is 
1.  2. 


1 

J  of  it? 
$  of  it? 

iof  it? 
iof  it? 


£  of  it? 

^of  it? 
iof  it? 


\  of  it? 


r  Of  it? 


of  it? 


3. 

A  of  it? 
A  of  it? 
^  of  it? 
A  of  it? 


U  of  it? 


4. 

A  of  it? 
A  of  it? 
A  of  it? 
A  of  it? 


What  per 

cent  of  a  number  is 

5. 

6. 

7. 

8. 

|  of  it? 

f  of  it? 

A  of  it? 

A  of  it? 

f  of  it? 

f  of  it? 

A  of  it? 

A  of  it? 

f  of  it? 

|  of  it? 

T3¥  of  it? 

A  of  it? 

f  of  it? 

|  of  it? 

A  of  it? 

A  of  it? 

|  of  it? 

|  of  it? 

Profit? 

A  of  it? 

f  of  it? 

A  of  it? 

A  of  it? 

A  of  it? 

f  of  it? 

A  of  it? 

A  of  it? 

A  of  it? 

What  per  cent  of  a  number  is 

9. 

Once  the  number? 
Twice  the  number? 

4  times  the  number? 
H  times  the  number? 

5  times  the  number? 


10. 

2\  times  the  number? 
8  times  the  number? 
\\  times  the  number  ? 
3  times  the  number? 
\\  times  the  number? 


What  per  cent 

11. 
Of  50  is  150? 
Of  40  is  60? 
Of  Yl\  is  50? 
Of  16  is  32? 


12. 

Of  80  is  400? 
Of  75  is  100? 
Of  60  is  80? 


PERCENTAGE  115 

What  part  of  a  number  is 

1.                                              2.  3. 

50%  of  it  ?                   33|%  of  it  ?  20%  of  it  ? 

25%  of  it  ?                    16f  %  of  it  ?  10%  of  it  ? 

12|%  of  it  ?                     8i%  of  it  ?  5%  of  it  ? 

6i%ofit?                      4%  of  it?  2i%ofit? 

14f  %  of  it  ?                       2%  of  it  ?  3£%  of  it  ? 

3%  of  it  ?                       1%  of  it  ?  100%  of  it  ? 


What  part  of  anything  is 

4.  5.  6. 

75%  of  it  ?  37^%  of  it  ?  70%  of  it  ? 

66f%  of  it  ?  87|%  of  it  ?  15%  of  it  ? 

40%  of  it  ?  30%  of  it  ?  80%  of  it  ? 

60%  of  it  ?  83^%  of  it  ?  24%  of  it  ? 

80%  of  it  ?  90%  of  it  ?  18f  %  of  it  ? 

28f  %  of  it  ?  62i%  of  it  ?  45%  of  it  ? 


What  part  of  a  number  is 

7.  8.  9. 

i%  of  it  ?  % %  of  it  ?  i%  of  it  ? 

f%ofit?  i%ofit?  i%ofit? 

|%ofit?  |%ofit?  i%ofit? 


How  many  times  a  number  is 

10.  11.  12. 

400%  of  it  ?  125%  of  it  ?  300%  of  it  ? 

200%  of  it  ?  300%  of  it  ?  275%  of  it  ? 

150%  of  it ?  450%  of  it?  100%  of  it? 


116 


PERCENTAGE 


The  number  sought  is  100%. 
What  is  the  number  of  which 


1. 

2. 

3. 

15  is  10%? 

72  is  50%? 

20  is  1%? 

25  is  12|%? 

10  is  16f%? 

10  is  4%  ? 

16  is  20%? 

11  is  25%? 

18  is  50%? 

12is8i%? 

4is2i%? 

9  is  33i%? 

6is4%? 

7is2%? 

12  is  5%  ? 

3is6i%? 

6  is  1%? 

7isl2|%? 

4  is  5%? 

45  is  100%? 

60  is  10%? 

16  is  33!%? 

15  is  20%? 

5  is  2*%? 

Find  the  number  of  which 

4. 

5. 

6. 

24  is  37^%. 

35  is  62i%. 

63  is  874%. 

60  is  75%. 

72  is  90%. 

18  is  45%. 

9  is  30%. 

16  is  80%. 

6  is  15%. 

50  is  66|%. 

12is37i%. 

40  is  8%. 

45  is  83|-%. 

4  is  40%. 

54  is  6%. 

90  is  60%. 

33  is  75%. 

48  is  1%. 

49  is  87i%. 

20  is  66|%. 

7  is  3i%. 

100  is  40%. 

42  is  70%. 

25  is  62i%. 

To  find :   The  sum 

of  which 

7. 

8. 

9. 

$50  is  125%. 

$26  is  200%. 

$120  is  133^%. 

$75  is  150%. 

$42  is  105%. 

$100  is  166f  %. 

$15  is  300%. 

$18  is  120%. 

$260  is  130%. 

$90  is  112i%. 

$36  is  300%. 

$150  is  125%. 

$84  is  175%. 

$50  is  250%. 

$240  is  160%. 

PERCENTAGE 


117 


What  is 

1. 

25%  of  $50? 

10%  of  $40? 

12|%of$64? 

33^%  of  $18? 

6i%of  $48? 

16|%of  $36? 

5%  of  $20? 

4%  of  $60? 


50%  of  32? 

20%  of  45? 

8£%of  24? 

11*%  of  63? 

5%  of  80? 

25%  of  28? 
14f%of  56? 
33^%  of  39? 


3 

l%of 
3%  of 
6%  of 
8%  of 
4%  of 
5%  of 
7%  of 
9%  of 


200? 

400? 

500? 

300? 

100? 

1000? 

2000? 

3000? 


nd 

4. 

5. 

6. 

75%  of  200. 

1%  of  $12. 

\\%  of  $400. 

66f  %  of  450. 

1%  of  $  1.50 

4^%  of  $200. 

37i%  of  160. 

.    1%  of  $  3.00 

2\%  of  $800. 

40%  of  250. 

1%  of  $  6.20 

3^%  of  $600. 

62i%  of  320. 

1%  of  $30. 

5i%  of  $100. 

87^%  of  240. 

1%  of  $25.50 

Si%  of  $2000. 

80%  of  400. 

1%  of  $  7.90 

6i%  of  $1000. 

83^%  of  300. 

l%of  $  1.25 

\\%  of  $4000. 

What  is 
7. 
\%  of  $1600? 
i%of$400? 
i%  of  $1000? 
i%of  $600? 

Tell  how  to  express  decimally 

10.  11. 

^  per  cent.         £  per  cent. 

\  per  cent.         \  per  cent. 


8. 

i%  of  $2000? 
1%  of  $1200? 
f%  of  $1500? 

f%of  $800? 


12. 

f  per  cent. 
§  per  cent. 


9. 

|%  of  $2400? 

A%  of  $2000? 

%%  of  $2500? 


13. 

f  per  cent, 
f  per  cent. 


118 


PERCENTAGE 


Increase  the  number 
1. 

12  by  50%. 

15  by  20%. 
20  by  10%. 

8  by  25%. 
6  by  33*%. 

16  by  12*%. 
18  by  16*%. 
24  by  8*%. 


40  by  20%. 
36  by  33*%. 
20  by  25%. 
100  by  1%. 
50  by  50%. 
25  by  4%. 
60  by  5%. 
32  by  6*%. 


35  by 
80  by 
45  by 
28  by 
70  by 
27  by 
30  by 
64  by 


14*%. 

5%. 

20%. 

25%. 

10%. 

33*%. 

16|%. 

12*%. 


Decrease  the  numoer 

4. 

5. 

6. 

10  by  20%. 

15  by  33*%. 

9  by  66f  %. 

20  by  5%. 

25  by  4%. 

12  by  75%. 

30  by  16f  %. 

36  by  25%. 

16  by  12*%. 

40  by  12*%. 

48  by  6*%. 

14  by  14f  %. 

50  by  50%. 

56  by  12*%. 

24  by  16|%. 

60  by  8*%. 

72  by  50%. 

18  by  33*%. 

70  by  14f  %. 

84  by  8*%. 

28  by  25%. 

80  by  6*%. 

96  by  16|%. 

32  by  6*%. 

Increase 


7. 


i. 

$64  by  25  per  cent. 
$48  by  16f  per  cent. 
$75  by  12  per  cent. 
$36  by  66f  per  cent. 
$50  by  6  per  cent. 


Decrease 

8. 
$100  by  15  per  cent. 
$120  by  50  per  cent. 
$250  by  40  per  cent. 
$320  by  37|  per  cent. 
$500  by  4  per  cent. 


PERCENTAGE 

119 

What  per  cent  is 

1. 

2. 

3. 

2  of  4? 

lof  5? 

$  3  of  $4? 

5  of  10? 

2  of  10? 

$  8  of  $12? 

3  of  12? 

8  of  4? 

$  9  of  $12? 

2  of  6? 

2  of  16? 

$  5  of  $25? 

lof  4? 

3  of  21? 

$  2  of  $3? 

9  of  3? 

2  of  20? 

$10  of  $4? 

15  of  5? 

30  of  10? 

$  3  of  $8? 

lof  2? 

10  of  20? 

$15  of  $10? 

What  per  cent  is 

4. 

5. 

6. 

25    of  50? 

33|-of  66f? 

25    of62±? 

12iof  25? 

8Jof  50? 

50    of  75? 

6iof  12i? 

12^  of  37^? 

12|  of  87i? 

37iof  75? 

16f  of  33±? 

6iof  50? 

6£of  25? 

25    of  75? 

25    of87i? 

12^  of  50? 

50    of62|? 

16|  of  66f  ? 

37£of  50? 

12$  of  62*  ? 

8Jof  25? 

8j'of  33|? 

8|of  16f? 

3£ofl0? 

Compare 

7. 
i  of  5000  people  with  \%  of  them, 
f  of  a  $1000  bond  with  f%  of  it. 
\  of  a  ton  of  coal  with  \%  of  it. 
f  of  your  weight  with  f  %  of  it. 
f  of  our  national  debt  with  f  %  of  it. 

What  ratio  does  the  first  answer  bear  to  the  second,  in  each  case  ? 


120         PERCENTAGE  AND  DENOMINATE  NUMBERS 

1.   A  pint  is  what  per  cent  of  a  quart? 
A  foot  is  what  per  cent  of  a  yard  ? 
A  nickel  is  what  per  cent  of  a  quarter? 
A  nickel  is  what  per  cent  of  a  dime? 
A  gill  is  what  per  cent  of  a  pint? 
A  quart  is  what  per  cent  of  a  gallon? 
A  cent  is  what  per  cent  of  a  dime? 
A  cent  is  what  per  cent  of  a  nickel? 
A  peck  is  what  per  cent  of  a  bushel? 
A  week  is  what  per  cent  of  a  fortnight  ? 


2.   What  per  cent  of  a  gallon  is  a  pint  ? 
What  per  cent  of  a  peck  is  a  quart  ? 
What  per  cent  of  a  foot  is  an  inch? 
What  per  cent  of  a  pound  is  an  ounce? 
What  per  cent  of  a  week  is  a  day? 
What  per  cent  of  a  year  is  a  month? 
What  per  cent  of  a  quart  is  a  gill? 
What  per  cent  of  a  peck  is  a  pint  ? 
What  per  cent  of  a  cord  is  a  cord  foot  ? 
What  per  cent  of  a  decade  is  a  year? 


To  the  Pupil:    Consult  your  dictionary  or  arithmetic  if  you  need 
help. 

3.  A  dozen  is  what  per  cent  of  a  gross  ? 
A  foot  is  what  per  cent  of  a  fathom? 
A  quarter  is  what  per  cent  of  a  year? 
A  hundred  weight  is  what  per  cent  of  a  ton? 
A  quire  is  what  per  cent  of  a  ream? 
A  cubic  foot  is  what  per  cent  of  a  cord  foot  ? 


PERCENTAGE  AND  DENOMINATE  NUMBERS         121 

1.  What  per  cent  of  a  gallon  is 

lqt.?     2qt.?     3qt.?     4qt.?     1  pt.?     3  pt.?     5pt.? 

2.  What  per  cent  of  a  pound  is 

8oz.?    4oz.?     12  oz.?     loz.?     2oz.?     6  oz.?     16  oz.? 

3.  What  per  cent  of  a  peck  is 

8qt.?    4qt.?     2qt.?     6q.?     lqt.?     7  qt.?     1  pt.? 

4. '  What  per  cent  of  a  ton  is 

500  1b.?    200  1b.?    1000  1b.?    15001b.?    201b.?     1001b.? 

5.  What  per  cent  of  a  day  is 

16  hr.?     12  hr.?     8hr.?     6hr.?     18  hr.?     3hr.?     9hr.? 

6.  What  per  cent  of  an  hour  is 

15min.?    12min.?    6min.?   40min.?  45  min.?   20min.? 

7.  What  per  cent  of  a  mile  is 

160  rd.?    40  rd.?     80  rd.?     240  rd.?     32  rd.?     120  rd.? 

8.  What  per  cent  of  a  dozen  is 

10  units?    9  units?    8  units?    4  units?    3  units?    2  units? 

9.  What  per  cent  of  a  right  angle  is 

90°?    45°?    30°?    60°?     18°?     15°?     75°?    27°? 

10.  What  per  cent  of  a  bushel  is 

16  qt.?     8qt.?     24  qt.?     1  pk.?    3pk.?    4pk.?     §  pk.? 

11.  What  per  cent  of  a  month  (30  days)  is 

10  da.?    6  da.?    15  da.?    20  da.?    3  da.?    5  da.?   24  da.? 


122         PERCENTAGE  AND   DENOMINATE  NUMBERS 


1. 


25%  of  a  peck 
50%  of  a  year 
50%  of  a  day 
25%  of  a  quart 
25%  of  a  yard 
75%  of  a  yard 
50%  of  a  pound 
75%  of  a  foot 


i  how  many 

■  how  many 

■  how  many 

■  how  many 
=  how  many 

■  how  many 
■■  how  many 
»  how  many 


quarts  ? 
months  ? 
hours  ? 
pints  ? 
inches  ? 
inches  ? 
ounces  ? 
inches  ? 


25%  of  an  acre 

50%  of  a  circumference 

75%  of  a  mile 

50%  of  a  leap-year 

25%  of  a  ton 

25%  of  a  square  foot 

75%  of  an  hour 

75%  of  a  dozen 


how  many  square  rods? 

how  many  degrees? 

how  many  rods? 
'  how  many  days? 

how  many  pounds? 

how  many  square  inches? 

how  many  minutes  ? 
«  how  many  things  ? 


3.   50%  of  a  bushel 
50%  of  a  mile 
25%  of  a  cord 
75%  of  an  acre 
50%  of  a  rt.  angle 
75%  of  a  gallon 
25%  of  a  square  mile 
75%  of  a  ream 


=  how  many  pints? 

=  how  many  feet  ? 

=  how  many  cubic  feet  ? 

=  how  many  square  rods? 

=  how  many  degrees? 

=  how  many  gills? 

=  how  many  acres  ? 

=  how  many  sheets  of  paper? 


PERCENTAGE  AND  DENOMINATE  NUMBERS         123 

1.  33  J  %  of  a  yard  =  how  many  inches? 
10%  of  a  minute  =  how  many  seconds? 
20%  of  a  quarter  =  how  many  cents  ? 
12  J%  of  a  pound  =  how  many  ounces? 
33  J  %  of  a  dozen  =  how  many  units? 
12|%  of  a  day  =  how  many  hours? 
16 f%  of  a  quire  =  how  many  sheets? 
20%  of  a  score  =  how  many  units  ? 

2.  66f  %  of  a  foot  =  how  many  inches? 
37  J  %  of  a  peck  =  how  many  quarts? 
60%  of  a  dime  =  how  many  cents? 
62|%  of  a  pound  =  how  many  ounces? 
84%  of  a  dozen  =  how  many  units? 
40%  of  an  hour  =  how  many  minutes? 
87|%  of  a  day  =  how  many  hours? 
6|%  of  a  pound  =  how  many  ounces? 

How  many  inches  in  How  many  square  inches  in 

3.   50%  of  a  yard?  4.   50%  of  a  square  foot ? 

25%  of  a  yard  ?  25%  of  a  square  foot  ? 

75%  of  a  yard?  75%  of  a  square  foot? 

33J%  of  a  yard ?  33 \%  of  a  square  foot  ? 

66f  %  of  a  yard  ?  66f  %  of  a  square  foot  ? 

8f%  of  a  yard  ?  16f %  of  a  square  foot  ? 

12|%  of  a  yard  ?  8J%  of  a  square  foot  ? 

37J%  of  a  yard?  12J%  of  a  square  foot? 

62|%  of  a  yard?  37-J%  of  a  square  foot? 

16f %  of  a  yard?  62|%  of  a  square  foot? 


124  SPEED   TESTS  IN  PERCENTAGE 

1.    28       2.    100       3.    18       4.    150       5.   80       6.   30       7.    100 

10  40  9  39  24  72  25 

2  8  33  24  40  6  40 

36  48  6  36  64  42  5 

18  32  21  60  16  18  35 

6  24  15  45  32  36  50 

50  4  90  12  48  60  10 

12  20  30  3  72  48  150 

22  44  75  48  8  12  75 

30  16  27  66  56  54  60 

Name  as  rapidly  as  you  can 

1.  50%  of  each  number  in  columns  1  and  2. 

2.  25%  of  each  number  in  column  2. 

3.  75%  of  each  number  in  column  2. 

4.  33  J  %  of  each  number  in  columns  3  and  4. 

5.  66f  %  of  each  number  in  column  3. 

6.  66f  %  of  each  number  in  column  4. 

7.  12J%  of  each  number  in  column  5. 

8.  37^%  of  each  number  in  column  5. 

9.  62|%  of  each  number  in  column  5. 

10.  87|  %  of  each  number  in  column  5. 

11.  16f  %  of  each  number  in  column  6. 

12.  83  J  %  of  each  number  in  column  6. 

13.  20%  of  each  number  in  column  7. 

14.  40%  of  each  number  in  column  7. 

15.  60%  of  each  number  in  column  7. 

16.  80%  of  each  number  in  column  7. 

17.  What  common  fractions  are  the  same  as  these  per  cents? 

10%  25%       12*%       8|%        33J%       75%        66f%       60% 

16f%  61%      40%        37|%       50%        87*%      20%        83*% 

30%  5%        80%        4%          70%         100%       14f%       90% 


AREAS  AND   PERIMETERS 


Find  area  and  perimeter  of 

1.   A  5-inch  square. 
A  10-inch  square. 
A  6-inch  square. 
A  9-inch  square. 
A  4-inch  square. 
A  3-foot  square. 
A  7-foot  square. 
A  12-foot  square. 
An  8-foot  square. 
An  11-foot  square. 


3.   What  is  the  perimeter  of 

A  rectangle  6"  X  4§"? 
A  rectangle  2}"  X  4"? 
A  rectangle  8"  X  1$"? 
A  rectangle  9"  x  2|"? 
A  rectangle  10"  X  5|"? 
An  oblong  1' X  i'? 
An  oblong  12'  x  15'? 
An  oblong  15'  x  20'? 
An  oblong  20' x  5'? 
An  oblong  30' x  2'? 


A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 
A  rectangle 


125 


5"  by  2". 
3"  by  7". 
4"  by  10". 
12"  by  1". 
8"  by  2". 
T  by  5'. 
2'  by  11'. 
10'  by  6'. 
9'  by  5'. 
4'  by  3'. 


A  5|" 
Al|" 


4.   What  is  the  area  of 

A  2J"  square? 
A  Z\"  square? 

square  ? 

square  ? 
A  4^"  square? 
A  20'  square? 
A  30'  square? 
A  2 ¥  square? 
A  10'  square? 
A  If  square? 


5.   Find  perimeter  and  area  of 

A  pasture  40  rods  square. 
A  garden  30  x  50  feet. 
A  building  lot  50  x  100  feet. 
A  playground  100  X  200  feet. 
A  park  25  x  30  rods. 


APPENDIX 

The  few  pages  which  follow  are  outside  the  plan  of  this  book,  but 
are  inserted  for  the  convenience  of  teachers  who  may  have  need  of 
such  material  as  they  contain. 

These  pages  are  nine  in  number : 

1.  Reading  Exercise,  Whole  Numbers. 

2.  Reading  Exercise,  Whole  Numbers. 

3.  Reading  Exercise,  U.  S.  Money. 

4.  Reading  Exercise,  Roman  Numerals. 

5.  Months  and  Dates. 

6.  Ratio,  and  its  Application  to  Simple  Problems. 

7.  Questions  for  Leisure  Moments. 

8.  Questions  for  Leisure  Moments. 

9.  Questions  for  Leisure  Moments. 


126 


READING    OF   WHOLE   NUMBERS 

1.  2,303  2.  5,012  3.  48,484       4.  31,527 

9,091  2,270  30,103  90,318 

8,808  8,008  67,380  66,123 

6,590  5,060  23,489  40,831 

7,227  9,876  41,707  28,506 

2,772  2,100  20,120  75,009 

5,099  4,404  11,006  40,040 

3,303  5,055  84,090  10,001 

8,017  6,600  10,005  56,950 

5,110  1,011  70,020  88,020 


207,840 

6.  408,123 

7.  4,000,000 

8.  5,100,004 

911,255 

73,240 

1,720,216 

236,600 

442,233 

81,006 

9,008,400 

82,503 

630,040 

428,820 

3,000,075 

261,599 

605,066 

60,075 

2,633,684 

8,084,302 

129,129 

900,009 

5,066,114 

62,001 

703,004 

71,032 

8,000,600 

777,666 

150,015 

3,890 

4,020,096 

5,200,048 

400,440 

154,400 

3,344,000 

137,425 

860,068 

76,000 

1,200,005 

50,606 

9.  23,640,125  10.  148,000,265       11.  13,605,400 

8,347,720  804,012,000  724,100,098 

91,100,042  160,006,060  5,000,225 

58,000,004  432,593,687  417,069,008 

3,374,810  220,000,220  24,403,100 

28,136,000  864,102,300  6,000,550 

1,012,012  521,000,336  920,109,111 

6,700,000  101,612,000  5,005,500 

25,025,009  254,369,845  612,018,000 

10,100,100  912,814,711  115,230,003 

127 


128  READING  OF  WHOLE  NUMBERS 

1.  1,001     2.  25,000     3.  105,675      4.  75,204 
7,240       10,204       920,043  3,319 


9. 


4,086 

91,900 

212,114 

600,420 

6,955 

80,075 

303,206 

80,307 

2,040 

30,006 

110,770 

2,925 

5,007 

22,401 

678,678 

405,060 

1,313 

67,809 

602,206 

77,440 

7,700 

56,078 

547,000 

3,802 

3,016 

30,456 

100,101 

745,010 

2,212 

70,700 

980,755 

604,288 

82,008     6, 

,  302,050 

7.  2,750,933 

8.  1,425,869 

50,403 

510,115 

3,861,002 

604,133 

27,011 

708,000 

5,409,080 

28,002 

19,222 

601,211 

1,000,040 

901,090 

77,001 

991,903 

7,032,006 

7,706,055 

40,020 

400,040 

6,448,000 

4,011 

25,025 

127,721 

1,020,703 

723,000 

50,250 

200,405 

4,307,618 

5,000,030 

16,161 

696,807 

9,000,750 

8,902,007 

80,505 

110,111 

6,300,003 

2,601 

35,127,950 

10. 

734,100,200 

11.   3,041,296 

4,000,306 

58,000,030 

733,155 

209,140,000 

163,302,445 

49,037,082 

18,018,200 

8,346,921 

200,000,360 

6,334,002 

542,806,009 

71,340,809 

20,000,020 

70,000,236 

4,502,075 

730,035,700 

5,024,000 

316,402 

2,200,200 

621,006 

44,389,600 

95,900,554 

940,032,065 

908,760,543 

105,002,007 

7,320,439 

27,140 

840,036 

24,706 

6,645,613 

9,237,540 

2,150,430 

54,903,027 

READING  EXERCISE     U.   S.  MONEY  129 

1.   $    8.36  2.   $  50.00  3.   $751.14             4.   $863.20 

51.25  250.00  45.50  20.25 

270.04  6.39  332.28  71.00 

7.20  40.88  88.40  301.12 

80.08  931.27  190.87  5.74 

44.21  804.05  345.68  36.95 

670.03  22.02  91.12  310.00 

,      9.27  150.16  171.80  65.05 

60.20  570.04  6.55  414.80 

488.34  39.00  18.42  50.50 


5. 


;     90.99 

6.   $   426.80 

7.   $  1,212.13 

8.   $51,502.36 

213.67 

5,019.05 

45,008.50 

7,243.68 

55.04 

100.84 

171.12 

44,000.00 

580.92 

2,971.70 

8,063.09 

2,063.24 

6,008.00 

4,222.04 

75,012.00 

751.25 

12.50 

68.25 

2,184.75 

2,002.40 

345.07 

6,120.00 

7,007.10 

40,321.21 

924.36 

466.00 

640.02 

6,780.09 

7,000.20 

7,280.15 

50.09 

818.58 

66.06 

3,000.95 

833.27 

11,010.04 

9.   $5,208,136.00  10.   $    543,287.10  11.    $  302,108.73 

42,020.12  2,040,069.52  99,053.06 

180,181.06  8,221.04  410,111.00 

76,000.40  95,095.16  7,005.02 

2,302,190.75  83,301.20  6,170,000.54 

8,009,  0  10  260  953.88  33,598.11 

78,403.00  5,000,275.00  4,080.08 

590,000.95  705,003.05  7,600,540.20 

3,000,625.70  1,009,008.60  50,050.50 

1,100,000.00  42,000.10  2,800.00 

55,209.38  317,700.25  5,000,439.80 

600,020.08  8,000,025.42  625,012.15 


130 


READING  EXERCISE     ROMAN  NUMERALS 


Note.  Ability  to  read  numbers  expressed  in  the  Roman  no- 
tation is  all  that  should  be  required  of  pupils,  and  but  little  time 
should  be  spent  even  in  reading  them. 

1=1.    V  -  5.    X  =  10.    L  =  50.    C  =  100.    D  -  500.    M  =  1000. 


1. 

2. 

3. 

4. 

5. 

6. 

I 

II 

ccc 

XII 

LXXX            XIV 

V 

III 

VI 

XIII 

IV 

XVI 

X 

XX 

VII 

XV 

IX 

XVII 

L 

XXX            VIII 

LX 

XL 

XVIII 

C 

cc 

XI 

LXX 

XC 

XIX 

7. 

8. 

9. 

10. 

XXI 

XXIV 

LV 

LXXI 

XXXI 

XXXII 

LXVI 

XCIV 

XLI 

XLIII 

LXXVII 

LIII 

LI 

LVIII 

LXXXII 

XLVII 

LXI 

LXVII 

XXVIII 

XXXV 

LXXI 

LXXIX 

XXXIX 

LXVIII 

LXXXI 

LXXXVI 

XLIV 

XXVI 

XCI 

XCV 

XCIII 

LXXXIX 

11. 

12. 

13. 

14. 

D 

MDCC 

DLXIV 

MLXVI 

M 

MDCCC 

CDIV 

MCCXV 

CD 

MCM 

ecu 

MDLXIV 

DC 

DCX 

DLV 

MDCXVI 

DCC 

CDIV 

MM 

MDCXX 

DCCC 

DCLXV 

MDLXV 

MDCCCXII 

CM 

CCCX 

CDL 

MCDXCII 

MD 

CDX 

CDXLIV 

MDCCLXXVI 

MCD 

DXLV 

DCLXVI 

MCMXIV 

MDC 

DLXV 

ML 

MCMXXI 

MONTHS  AND  DATES 


131 


1.   What  is  the  first  month  of  the  year? 
The  twelfth?  The  sixth? 


The  eleventh  ? 
The  fifth? 

The  fourth? 


The  third? 
The  tenth? 


The  second? 
The  seventh? 
The  eighth? 
The  ninth? 


2.  Which  month  of  the  year  is 

October?  June?  December? 

February?  March?  April? 

November?  August?  January? 

3.  Memorize  these  two  lines : 


May? 
July? 
September  ? 


"  Thirty  days  hath  September, 
April,  June,  and  November." 

4.  Name  the  month  that  has  the  fewest  days.     How  many 
days  has  this  month  ? 

5.  All  the  months  not  named  above  have  thirty-one  days. 
Name  them. 


6.   On  business  papers,  the  month  is  often  expressed  by  a  nu- 
meral, and  the  year  abbreviated,  thus : 


2/24/05 
5/15/12 
8/26/09 

4/17/11 


1/5/18 
10/26/14 
7/12/15 
3/30/16 


7.   Express  in  numerals,  as  above  : 
Oct.  10,  1919  Feb.  22,  1920 


July  4,  1915 
March  23,  1900 


Dec.  18,  1916 
May  7,  1910 


11/8/20 
9/12/10 

12/25/17 
6/10/21 


Aug.  6,  1920 
Apr.  1,  1918 
June  18,  1921 


132 


RELATION  OF  NUMBERS,   OR  RATIO 


The  ratio  of  one  number  to  another  is  the  quotient  of  the  first 
divided  by  the  second. 


What  is  the  ratio  of 

1.   20  dollars  to  4  dollars? 
40  quarts  to  8  quarts? 
30  inches  to  6  inches  ? 
25  pounds  to  75  pounds  ? 
12  ounces  to  48  ounces? 

What  is  the  ratio  of 

3.   An  inch  to  a  foot  ? 
A  foot  to  a  yard? 
A  quart  to  a  gallon? 
A  day  to  a  week? 
An  ounce  to  a  pound  ? 

What  is  the  ratio  of 

5.   4  ounces  to  2  pounds? 
3  pints  to  3  quarts  ? 

5  months  to  2\  years? 

6  minutes  to  half  an  hour? 


21  cents  to  7  cents? 
9  yards  to  27  yards? 

8  acres  to  12  acres? 
6  days  to  8  days? 

9  tons  to  12  tons? 


A  foot  to  4  inches? 
A  pound  to  8  ounces 
A  day  to  6  hours? 
An  hour  to  15  minutes 
A  year  to  3  months? 


6.   2  dozen  units  to  8  units  ? 
5  years  to  10  months  ? 
4  pecks  to  4  quarts  ? 
1  yard  to  1J  feet? 


Application  of  Ratio 

Pupils  should  be  taught  to  solve  by  means  of  ratio  all  such  problems 
as  the  following  : 

If  5  quarts  of  milk  cost  80  cents,  how  much  will  10  quarts  cost  ? 
(It  is  not  necessary  to  find  the  cost  of  1  quart.) 

If  a  man's  salary  is  $3600  a  year,  how  much  does  he  earn  in 
4  months?     (Do  not  find  salary  for  1  month.) 

How  much  will  a  dozen  apples  cost  at  the  rate  of  3  for  ten  cents  ? 
{What  is  the  ratio  of  12  to  3?) 


QUESTIONS  FOR  LEISURE  MOMENTS  133 

Questions  for  Leisure  Moments 

To  pupils :  A  study  of  the  following  questions,  one  or  two  at  a 
time,  will  give  you  a  small  fund  of  useful  information  on  everyday 
subjects.  The  information  is  to  be  found  in  your  arithmetic  or  in  the 
dictionary. 

1.  How  long  is  a  fortnight?    A  quarter?    A  decade? 

2.  What  does  bi-weekly  mean ?     Bi-monthly? 

3.  How  many  is  three-score  and  ten? 

4.  Is  a  quart,  liquid  measure,  just  equal  to  a  quart,  dry 
measure  ?    Find  out  from  the  facts  given  here : 

The  standard  gallon  contains  231  cubic  inches. 
The  standard  bushel  contains  2150.42  cubic  inches. 

5.  What  is  the  difference  in  pounds  between  the  long  ton  and 
the  short  ton?  Which  one  is  commonly  used  in  the  United 
States?    In  England? 

6.  How  many  gallons  does  a  barrel  contain?    A  hogshead? 

7.  Give  the  dimensions  of  a  cord  of  wood.  Into  what  lengths 
is  the  wood  sawed? 

8.  How  is  lumber  sold?  What  does  the  abbreviation  "M" 
stand  for  ? 

9.  How  many  acres  in  a  square  mile? 

10.  How  deep  is  a  fathom? 

11.  How  long  is  a  league?  What  is  this  unit  of  measure  used 
for? 

12.  In  measuring  the  earth  removed  in  excavations,  how  much 
is  called  a  load? 


134  QUESTIONS  FOR  LEISURE  MOMENTS 

13.  How  large  is  a  township?    A  section?    Where  are  these 
terms  chiefly  used  ? 

14.  How  many  quires  of  paper  make  a  ream? 

15.  How  many  units  make  a  gross ?    A  great  gross? 

16.  How  can  the  leap  years  be  determined? 

17.  How  much  U  S.  money  is  equivalent  to  the  English  pound  ? 
To  the  French  franc?    To  the  German  mark? 

18.  Is  the  English  penny  equal  in  value  to  the  United  States 
cent?    Find  out  from  this  table : 

12  pence  (pennies)  make  1  shilling. 
20  shillings  make  1  pound. 

19.  Canada  is  a  province  of  Great  Britain.    Do  Canadians  use 
English  money? 

20.  What  is  a  ten-dollar  gold  piece  called?    A  twenty-dollar 
gold  piece  ? 

21.  Are  our  gold  and  silver  coins  made  of  the  pure  metal? 

22.  Name  the  coins  of  the  United  States,  and  the  metal  of  which 
each  is  made. 

23.  18-carat  gold  is  what  per  cent  pure  gold?    What  per  cent 
alloy  ? 

24.  What  does  the  word  "perimeter"  mean? 

25.  What  is  the  perimeter  of  a  circle  called? 

26.  What  relation  has  the  radius  of  a  circle  to  the  diameter? 
What  relation  has  the  diameter  to  the  circumference  ? 


QUESTIONS  FOR  LEISURE  MOMENTS  135 

27.  We  measure  distances  on  land  by  the  English  mile.     What 
is  the  length  of  this  mile  in  feet  ? 

28.  The  speed  of  a  vessel  is  measured  in  knots,  or  nautical 
miles.     A  nautical  mile  is  how  many  feet? 

29.  What  is  a  lunar  month?     A  calendar  month?     Which  is 
the  longer? 

30.  Explain  local  time,  and  standard  time.     Is  it  possible  for 
local  and  standard  time  to  correspond  at  any  place? 

31.  Which  unit  of  measure  is  longer,  the  meter  or  the  yard? 
How  much  longer? 

32.  How  was  the  length  of  the  meter  established? 

33.  In  what  countries  is  the  Metric  System  of  Weights  and 
Measures  commonly  used? 

34.  What  is  the  unit  of  weight  by  which  diamonds  and  other 
precious  stones  are  weighed  ? 

35.  What  are  safe  and  proper  ways  of  sending  money  to  a  person 
in  another  city  or  town  ? 

36.  Should  money  ever  be  inclosed  in  a  letter? 

37.  What  does  the  abbreviation  "Inc."  after  the  name  of  a 
business  firm  mean? 

38.  Generally  speaking,  is  it  safer  to  invest  money  in  stocks  or 
in  bonds?    Why? 


J  U>     OvJU/CJ 


075844 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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